---
_id: '11842'
abstract:
- lang: eng
text: We consider the flow of two viscous and incompressible fluids within a bounded
domain modeled by means of a two-phase Navier–Stokes system. The two fluids are
assumed to be immiscible, meaning that they are separated by an interface. With
respect to the motion of the interface, we consider pure transport by the fluid
flow. Along the boundary of the domain, a complete slip boundary condition for
the fluid velocities and a constant ninety degree contact angle condition for
the interface are assumed. In the present work, we devise for the resulting evolution
problem a suitable weak solution concept based on the framework of varifolds and
establish as the main result a weak-strong uniqueness principle in 2D. The proof
is based on a relative entropy argument and requires a non-trivial further development
of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech.
Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects
of the necessarily singular geometry of the evolving fluid domains, we work for
simplicity in the regime of same viscosities for the two fluids.
acknowledgement: The authors warmly thank their former resp. current PhD advisor Julian
Fischer for the suggestion of this problem and for valuable initial discussions
on the subjects of this paper. This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1
– 390685813.
article_number: '93'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation
for two fluids with ninety degree contact angle and same viscosities. Journal
of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2
apa: Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2
chicago: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same
Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature,
2022. https://doi.org/10.1007/s00021-022-00722-2.
ieee: S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities,”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature,
2022.
ista: Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. 24(3), 93.
mla: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature,
2022, doi:10.1007/s00021-022-00722-2.
short: S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).
corr_author: '1'
date_created: 2022-08-14T22:01:45Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00021-022-00722-2
ec_funded: 1
external_id:
arxiv:
- '2112.11154'
isi:
- '000834834300001'
file:
- access_level: open_access
checksum: 75c5f286300e6f0539cf57b4dba108d5
content_type: application/pdf
creator: cchlebak
date_created: 2022-08-16T06:55:22Z
date_updated: 2022-08-16T06:55:22Z
file_id: '11848'
file_name: 2022_JMathFluidMech_Hensel.pdf
file_size: 2045570
relation: main_file
success: 1
file_date_updated: 2022-08-16T06:55:22Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Mathematical Fluid Mechanics
publication_identifier:
eissn:
- 1422-6952
issn:
- 1422-6928
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '14587'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety
degree contact angle and same viscosities
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 24
year: '2022'
...
---
_id: '14597'
abstract:
- lang: eng
text: "Phase-field models such as the Allen-Cahn equation may give rise to the formation
and evolution of geometric shapes, a phenomenon that may be analyzed rigorously
in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn
equation with a potential with N≥3 distinct minima has been conjectured to describe
the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn
the present work, we give a rigorous proof for this statement in two and three
ambient dimensions and for a suitable class of potentials: As long as a strong
solution to multiphase mean curvature flow exists, solutions to the vectorial
Allen-Cahn equation with well-prepared initial data converge towards multiphase
mean curvature flow in the limit of vanishing interface width parameter ε↘0. We
even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the
gradient flow structure of the Allen-Cahn equation and its limiting motion: Building
on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature
flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation
with multi-well potential. This enables us to overcome the limitations of other
approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn
operator or additional convergence hypotheses for the energy at positive times."
article_number: '2203.17143'
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143
apa: Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the
vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv.
https://doi.org/10.48550/ARXIV.2203.17143
chicago: Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the
Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv,
n.d. https://doi.org/10.48550/ARXIV.2203.17143.
ieee: J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial
Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .
ista: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv, 2203.17143.
mla: Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial
Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, 2203.17143,
doi:10.48550/ARXIV.2203.17143.
short: J.L. Fischer, A. Marveggio, ArXiv (n.d.).
corr_author: '1'
date_created: 2023-11-23T09:30:02Z
date_published: 2022-03-31T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '31'
department:
- _id: JuFi
doi: 10.48550/ARXIV.2203.17143
ec_funded: 1
external_id:
arxiv:
- '2203.17143'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2203.17143
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: draft
related_material:
record:
- id: '17481'
relation: later_version
status: public
- id: '14587'
relation: dissertation_contains
status: public
status: public
title: Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase
mean curvature flow
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '10575'
abstract:
- lang: eng
text: The choice of the boundary conditions in mechanical problems has to reflect
the interaction of the considered material with the surface. Still the assumption
of the no-slip condition is preferred in order to avoid boundary terms in the
analysis and slipping effects are usually overlooked. Besides the “static slip
models”, there are phenomena that are not accurately described by them, e.g. at
the moment when the slip changes rapidly, the wall shear stress and the slip can
exhibit a sudden overshoot and subsequent relaxation. When these effects become
significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical
analysis of Navier–Stokes-like problems with a dynamic slip boundary condition,
which requires a proper generalization of the Gelfand triplet and the corresponding
function space setting.
acknowledgement: The research of A. Abbatiello is supported by Einstein Foundation,
Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical
Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No.
20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the
Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support
from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Anna
full_name: Abbatiello, Anna
last_name: Abbatiello
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
citation:
ama: Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied
Sciences. 2021;31(11):2165-2212. doi:10.1142/S0218202521500470
apa: Abbatiello, A., Bulíček, M., & Maringová, E. (2021). On the dynamic slip
boundary condition for Navier-Stokes-like problems. Mathematical Models and
Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500470
chicago: Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic
Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models
and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500470.
ieee: A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary
condition for Navier-Stokes-like problems,” Mathematical Models and Methods
in Applied Sciences, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212,
2021.
ista: Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition
for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences.
31(11), 2165–2212.
mla: Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like
Problems.” Mathematical Models and Methods in Applied Sciences, vol. 31,
no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:10.1142/S0218202521500470.
short: A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods
in Applied Sciences 31 (2021) 2165–2212.
date_created: 2021-12-26T23:01:27Z
date_published: 2021-10-13T00:00:00Z
date_updated: 2025-04-15T08:31:30Z
day: '13'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1142/S0218202521500470
external_id:
arxiv:
- '2009.09057'
isi:
- '000722309400001'
file:
- access_level: open_access
checksum: 8c0a9396335f0b70e1f5cbfe450a987a
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T10:55:45Z
date_updated: 2022-05-16T10:55:45Z
file_id: '11385'
file_name: 2021_MathModelsMethods_Abbatiello.pdf
file_size: 795483
relation: main_file
success: 1
file_date_updated: 2022-05-16T10:55:45Z
has_accepted_license: '1'
intvolume: ' 31'
isi: 1
issue: '11'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 2165-2212
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1245
name: Dissipation and dispersion in nonlinear partial differential equations
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the dynamic slip boundary condition for Navier-Stokes-like problems
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 31
year: '2021'
...
---
_id: '10005'
abstract:
- lang: eng
text: We study systems of nonlinear partial differential equations of parabolic
type, in which the elliptic operator is replaced by the first-order divergence
operator acting on a flux function, which is related to the spatial gradient of
the unknown through an additional implicit equation. This setting, broad enough
in terms of applications, significantly expands the paradigm of nonlinear parabolic
problems. Formulating four conditions concerning the form of the implicit equation,
we first show that these conditions describe a maximal monotone p-coercive graph.
We then establish the global-in-time and large-data existence of a (weak) solution
and its uniqueness. To this end, we adopt and significantly generalize Minty’s
method of monotone mappings. A unified theory, containing several novel tools,
is developed in a way to be tractable from the point of view of numerical approximations.
acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No.
18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges
support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583
by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian
Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers
of the Nečas Center for Mathematical Modelling.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
- first_name: Josef
full_name: Málek, Josef
last_name: Málek
citation:
ama: Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with
implicit constitutive equations involving flux. Mathematical Models and Methods
in Applied Sciences. 2021;31(09). doi:10.1142/S0218202521500457
apa: Bulíček, M., Maringová, E., & Málek, J. (2021). On nonlinear problems of
parabolic type with implicit constitutive equations involving flux. Mathematical
Models and Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500457
chicago: Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems
of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical
Models and Methods in Applied Sciences. World Scientific Publishing, 2021.
https://doi.org/10.1142/S0218202521500457.
ieee: M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic
type with implicit constitutive equations involving flux,” Mathematical Models
and Methods in Applied Sciences, vol. 31, no. 09. World Scientific Publishing,
2021.
ista: Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic
type with implicit constitutive equations involving flux. Mathematical Models
and Methods in Applied Sciences. 31(09).
mla: Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit
Constitutive Equations Involving Flux.” Mathematical Models and Methods in
Applied Sciences, vol. 31, no. 09, World Scientific Publishing, 2021, doi:10.1142/S0218202521500457.
short: M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied
Sciences 31 (2021).
date_created: 2021-09-12T22:01:25Z
date_published: 2021-08-25T00:00:00Z
date_updated: 2025-05-14T10:50:14Z
day: '25'
department:
- _id: JuFi
doi: 10.1142/S0218202521500457
external_id:
arxiv:
- '2009.06917'
isi:
- '000722222900004'
intvolume: ' 31'
isi: 1
issue: '09'
keyword:
- Nonlinear parabolic systems
- implicit constitutive theory
- weak solutions
- existence
- uniqueness
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2009.06917
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: On nonlinear problems of parabolic type with implicit constitutive equations
involving flux
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2021'
...
---
_id: '10549'
abstract:
- lang: eng
text: We derive optimal-order homogenization rates for random nonlinear elliptic
PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely,
for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially
homogeneous statistics) and fast decay of correlations on scales larger than the
microscale \varepsilon >0, we establish homogenization error estimates of the
order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon
|^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have
been limited to a small algebraic rate of convergence \varepsilon ^\delta . We
also establish error estimates for the approximation of the homogenized operator
by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for
a representative volume of size L. Our results also hold in the case of systems
for which a (small-scale) C^{1,\alpha } regularity theory is available.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) – project number 405009441.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Stefan
full_name: Neukamm, Stefan
last_name: Neukamm
citation:
ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational
Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9
apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9
chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in
Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.”
Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9.
ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic
homogenization of nonlinear uniformly elliptic equations and systems,” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp.
343–452, 2021.
ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization
of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics
and Analysis. 242(1), 343–452.
mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic
Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive
for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021,
pp. 343–452, doi:10.1007/s00205-021-01686-9.
short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242
(2021) 343–452.
date_created: 2021-12-16T12:12:33Z
date_published: 2021-06-30T00:00:00Z
date_updated: 2023-08-17T06:23:21Z
day: '30'
ddc:
- '530'
department:
- _id: JuFi
doi: 10.1007/s00205-021-01686-9
external_id:
arxiv:
- '1908.02273'
isi:
- '000668431200001'
file:
- access_level: open_access
checksum: cc830b739aed83ca2e32c4e0ce266a4c
content_type: application/pdf
creator: cchlebak
date_created: 2021-12-16T14:58:08Z
date_updated: 2021-12-16T14:58:08Z
file_id: '10558'
file_name: 2021_ArchRatMechAnalysis_Fischer.pdf
file_size: 1640121
relation: main_file
success: 1
file_date_updated: 2021-12-16T14:58:08Z
has_accepted_license: '1'
intvolume: ' 242'
isi: 1
issue: '1'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 343-452
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly
elliptic equations and systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 242
year: '2021'
...
---
_id: '8792'
abstract:
- lang: eng
text: This paper is concerned with a non-isothermal Cahn-Hilliard model based on
a microforce balance. The model was derived by A. Miranville and G. Schimperna
starting from the two fundamental laws of Thermodynamics, following M. Gurtin's
two-scale approach. The main working assumptions are made on the behaviour of
the heat flux as the absolute temperature tends to zero and to infinity. A suitable
Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary
value problem associated to the entropy formulation and, in a subcase, also to
the weak formulation of the model is proved by deriving suitable a priori estimates
and by showing weak sequential stability of families of approximating solutions.
At last, some highlights are given regarding a possible approximation scheme compatible
with the a-priori estimates available for the system.
acknowledgement: G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale
per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto
Nazionale di Alta Matematica).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
- first_name: Giulio
full_name: Schimperna, Giulio
last_name: Schimperna
citation:
ama: Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on
a microforce balance. Journal of Differential Equations. 2021;274(2):924-970.
doi:10.1016/j.jde.2020.10.030
apa: Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard
model based on a microforce balance. Journal of Differential Equations.
Elsevier. https://doi.org/10.1016/j.jde.2020.10.030
chicago: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard
Model Based on a Microforce Balance.” Journal of Differential Equations.
Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030.
ieee: A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based
on a microforce balance,” Journal of Differential Equations, vol. 274,
no. 2. Elsevier, pp. 924–970, 2021.
ista: Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based
on a microforce balance. Journal of Differential Equations. 274(2), 924–970.
mla: Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard
Model Based on a Microforce Balance.” Journal of Differential Equations,
vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030.
short: A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021)
924–970.
date_created: 2020-11-22T23:01:26Z
date_published: 2021-02-15T00:00:00Z
date_updated: 2025-07-10T12:01:25Z
day: '15'
department:
- _id: JuFi
doi: 10.1016/j.jde.2020.10.030
external_id:
arxiv:
- '2004.02618'
isi:
- '000600845300023'
intvolume: ' 274'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2004.02618
month: '02'
oa: 1
oa_version: Preprint
page: 924-970
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On a non-isothermal Cahn-Hilliard model based on a microforce balance
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 274
year: '2021'
...
---
_id: '9240'
abstract:
- lang: eng
text: A stochastic PDE, describing mesoscopic fluctuations in systems of weakly
interacting inertial particles of finite volume, is proposed and analysed in any
finite dimension . It is a regularised and inertial version of the Dean–Kawasaki
model. A high-probability well-posedness theory for this model is developed. This
theory improves significantly on the spatial scaling restrictions imposed in an
earlier work of the same authors, which applied only to significantly larger particles
in one dimension. The well-posedness theory now applies in d-dimensions when the
particle-width ϵ is proportional to for and N is the number of particles. This
scaling is optimal in a certain Sobolev norm. Key tools of the analysis are fractional
Sobolev spaces, sharp bounds on Bessel functions, separability of the regularisation
in the d-spatial dimensions, and use of the Faà di Bruno's formula.
acknowledgement: All authors thank the anonymous referee for his/her careful reading
of the manuscript and valuable suggestions. This paper was motivated by stimulating
discussions at the First Berlin–Leipzig Workshop on Fluctuating Hydrodynamics in
August 2019 with Ana Djurdjevac, Rupert Klein and Ralf Kornhuber. JZ gratefully
acknowledges funding by a Royal Society Wolfson Research Merit Award. FC gratefully
acknowledges funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 2021;284(5):253-283. doi:10.1016/j.jde.2021.02.048
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2021). Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2021.02.048
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “Well-Posedness
for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several
Space Dimensions.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2021.02.048.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions,”
Journal of Differential Equations, vol. 284, no. 5. Elsevier, pp. 253–283,
2021.
ista: Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 284(5), 253–283.
mla: Cornalba, Federico, et al. “Well-Posedness for a Regularised Inertial Dean–Kawasaki
Model for Slender Particles in Several Space Dimensions.” Journal of Differential
Equations, vol. 284, no. 5, Elsevier, 2021, pp. 253–83, doi:10.1016/j.jde.2021.02.048.
short: F. Cornalba, T. Shardlow, J. Zimmer, Journal of Differential Equations 284
(2021) 253–283.
date_created: 2021-03-14T23:01:32Z
date_published: 2021-05-25T00:00:00Z
date_updated: 2025-04-14T07:43:51Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2021.02.048
ec_funded: 1
external_id:
isi:
- '000634823300010'
file:
- access_level: open_access
checksum: c630b691fb9e716b02aa6103a9794ec8
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T07:18:01Z
date_updated: 2021-03-22T07:18:01Z
file_id: '9267'
file_name: 2021_JourDiffEquations_Cornalba.pdf
file_size: 473310
relation: main_file
success: 1
file_date_updated: 2021-03-22T07:18:01Z
has_accepted_license: '1'
intvolume: ' 284'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 253-283
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles
in several space dimensions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 284
year: '2021'
...
---
_id: '9307'
abstract:
- lang: eng
text: We establish finite time extinction with probability one for weak solutions
of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with
Stratonovich transport noise and compactly supported smooth initial datum. Heuristically,
this is expected to hold because Brownian motion has average spread rate O(t12)
whereas the support of solutions to the deterministic PME grows only with rate
O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent
shift for Wong–Zakai type approximations, the transformation to a deterministic
PME with two copies of a Brownian path as the lateral boundary, and techniques
from the theory of viscosity solutions.
acknowledgement: This project has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem
as well as helpful discussions. Special thanks go to F. Cornalba for suggesting
the additional κ-truncation in Proposition 5. I am also indebted to an anonymous
referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning
the treatment of the noise term). The issue is resolved in this version.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Finite time extinction for the 1D stochastic porous medium equation
with transport noise. Stochastics and Partial Differential Equations: Analysis
and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9'
apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9'
chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous
Medium Equation with Transport Noise.” Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.'
ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation
with transport noise,” Stochastics and Partial Differential Equations: Analysis
and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.'
ista: 'Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. 9, 892–939.'
mla: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium
Equation with Transport Noise.” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.'
short: 'S. Hensel, Stochastics and Partial Differential Equations: Analysis and
Computations 9 (2021) 892–939.'
date_created: 2021-04-04T22:01:21Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2025-03-31T16:00:58Z
day: '21'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-021-00188-9
ec_funded: 1
external_id:
isi:
- '000631001700001'
file:
- access_level: open_access
checksum: 6529b609c9209861720ffa4685111bc6
content_type: application/pdf
creator: dernst
date_created: 2021-04-06T09:31:28Z
date_updated: 2021-04-06T09:31:28Z
file_id: '9309'
file_name: 2021_StochPartDiffEquation_Hensel.pdf
file_size: 727005
relation: main_file
success: 1
file_date_updated: 2021-04-06T09:31:28Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 892–939
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finite time extinction for the 1D stochastic porous medium equation with transport
noise
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2021'
...
---
_id: '9335'
abstract:
- lang: eng
text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon:
depending on the “flatness” of the compactly supported initial datum at the boundary
of the support, the support of the solution may not expand for a certain amount
of time. We show that this phenomenon is captured by particular Lagrangian discretizations
of the porous medium and the thin film equations, and we obtain sufficient criteria
for the occurrence of waiting times that are consistent with the known ones for
the original PDEs. For the spatially discrete solution, the waiting time phenomenon
refers to a deviation of the edge of support from its original position by a quantity
comparable to the mesh width, over a mesh-independent time interval. Our proof
is based on estimates on the fluid velocity in Lagrangian coordinates. Combining
weighted entropy estimates with an iteration technique à la Stampacchia leads
to upper bounds on free boundary propagation. Numerical simulations show that
the phenomenon is already clearly visible for relatively coarse discretizations.'
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109, “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Daniel
full_name: Matthes, Daniel
last_name: Matthes
citation:
ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis.
2021;59(1):60-87. doi:10.1137/19M1300017
apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially
discretized porous medium and thin film equations. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017
chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in
Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1300017.
ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized
porous medium and thin film equations,” SIAM Journal on Numerical Analysis,
vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021.
ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1),
60–87.
mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially
Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical
Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics,
2021, pp. 60–87, doi:10.1137/19M1300017.
short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87.
date_created: 2021-04-18T22:01:42Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-08T13:10:40Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/19M1300017
external_id:
arxiv:
- '1911.04185'
isi:
- '000625044600003'
intvolume: ' 59'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1911.04185
month: '01'
oa: 1
oa_version: Preprint
page: 60-87
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The waiting time phenomenon in spatially discretized porous medium and thin
film equations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
_id: '9352'
abstract:
- lang: eng
text: This paper provides an a priori error analysis of a localized orthogonal decomposition
method for the numerical stochastic homogenization of a model random diffusion
problem. If the uniformly elliptic and bounded random coefficient field of the
model problem is stationary and satisfies a quantitative decorrelation assumption
in the form of the spectral gap inequality, then the expected $L^2$ error of the
method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$,
$\varepsilon$ being the small correlation length of the random coefficient and
$H$ the width of the coarse finite element mesh that determines the spatial resolution.
The proof bridges recent results of numerical homogenization and quantitative
stochastic homogenization.
acknowledgement: 'This work was initiated while the authors enjoyed the kind hospitality
of the Hausdorff Institute for Mathematics in Bonn during the trimester program
Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim
would like to acknowledge the kind hospitality of the Erwin Schrödinger International
Institute for Mathematics and Physics (ESI), where parts of this research were
developed under the frame of the thematic program Numerical Analysis of Complex
PDE Models in the Sciences.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Dietmar
full_name: Gallistl, Dietmar
last_name: Gallistl
- first_name: Dietmar
full_name: Peterseim, Dietmar
last_name: Peterseim
citation:
ama: Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 2021;59(2):660-674.
doi:10.1137/19M1308992
apa: Fischer, J. L., Gallistl, D., & Peterseim, D. (2021). A priori error analysis
of a numerical stochastic homogenization method. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1308992
chicago: Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error
Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1308992.
ieee: J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of
a numerical stochastic homogenization method,” SIAM Journal on Numerical Analysis,
vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021.
ista: Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical
stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674.
mla: Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic
Homogenization Method.” SIAM Journal on Numerical Analysis, vol. 59, no.
2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:10.1137/19M1308992.
short: J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis
59 (2021) 660–674.
date_created: 2021-04-25T22:01:31Z
date_published: 2021-03-09T00:00:00Z
date_updated: 2023-08-08T13:13:37Z
day: '09'
department:
- _id: JuFi
doi: 10.1137/19M1308992
external_id:
arxiv:
- '1912.11646'
isi:
- '000646030400003'
intvolume: ' 59'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1912.11646
month: '03'
oa: 1
oa_version: Preprint
page: 660-674
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A priori error analysis of a numerical stochastic homogenization method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...
---
OA_place: publisher
_id: '10007'
abstract:
- lang: eng
text: The present thesis is concerned with the derivation of weak-strong uniqueness
principles for curvature driven interface evolution problems not satisfying a
comparison principle. The specific examples being treated are two-phase Navier-Stokes
flow with surface tension, modeling the evolution of two incompressible, viscous
and immiscible fluids separated by a sharp interface, and multiphase mean curvature
flow, which serves as an idealized model for the motion of grain boundaries in
an annealing polycrystalline material. Our main results - obtained in joint works
with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation
of geometric singularities due to topology changes, the weak solution concept
of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with
surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial
Differential Equations 55, 2016) to multiphase mean curvature flow (for networks
in R^2 or double bubbles in R^3) represents the unique solution to these interface
evolution problems within the class of classical solutions, respectively. To the
best of the author's knowledge, for interface evolution problems not admitting
a geometric comparison principle the derivation of a weak-strong uniqueness principle
represented an open problem, so that the works contained in the present thesis
constitute the first positive results in this direction. The key ingredient of
our approach consists of the introduction of a novel concept of relative entropies
for a class of curvature driven interface evolution problems, for which the associated
energy contains an interfacial contribution being proportional to the surface
area of the evolving (network of) interface(s). The interfacial part of the relative
entropy gives sufficient control on the interface error between a weak and a classical
solution, and its time evolution can be computed, at least in principle, for any
energy dissipating weak solution concept. A resulting stability estimate for the
relative entropy essentially entails the above mentioned weak-strong uniqueness
principles. The present thesis contains a detailed introduction to our relative
entropy approach, which in particular highlights potential applications to other
problems in curvature driven interface evolution not treated in this thesis.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Curvature driven interface evolution: Uniqueness properties of weak
solution concepts. 2021. doi:10.15479/at:ista:10007'
apa: 'Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007'
chicago: 'Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021.
https://doi.org/10.15479/at:ista:10007.'
ieee: 'S. Hensel, “Curvature driven interface evolution: Uniqueness properties of
weak solution concepts,” Institute of Science and Technology Austria, 2021.'
ista: 'Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria.'
mla: 'Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts. Institute of Science and Technology Austria, 2021,
doi:10.15479/at:ista:10007.'
short: 'S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of
Weak Solution Concepts, Institute of Science and Technology Austria, 2021.'
corr_author: '1'
date_created: 2021-09-13T11:12:34Z
date_published: 2021-09-14T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '14'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:10007
ec_funded: 1
file:
- access_level: closed
checksum: c8475faaf0b680b4971f638f1db16347
content_type: application/x-zip-compressed
creator: shensel
date_created: 2021-09-13T11:03:24Z
date_updated: 2021-09-15T14:37:30Z
file_id: '10008'
file_name: thesis_final_Hensel.zip
file_size: 15022154
relation: source_file
- access_level: open_access
checksum: 1a609937aa5275452822f45f2da17f07
content_type: application/pdf
creator: shensel
date_created: 2021-09-13T14:18:56Z
date_updated: 2021-09-14T09:52:47Z
file_id: '10014'
file_name: thesis_final_Hensel.pdf
file_size: 6583638
relation: main_file
file_date_updated: 2021-09-15T14:37:30Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '300'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10012'
relation: part_of_dissertation
status: public
- id: '10013'
relation: part_of_dissertation
status: public
- id: '7489'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: 'Curvature driven interface evolution: Uniqueness properties of weak solution
concepts'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '10013'
abstract:
- lang: eng
text: We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction of a gradient-flow calibration in the sense
of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster.
This extends the two-dimensional construction to the three-dimensional case of
surfaces meeting along triple junctions.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
article_number: '2108.01733'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
citation:
ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv. doi:10.48550/arXiv.2108.01733
apa: Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature
flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” arXiv. .
ista: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv, 2108.01733.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.
short: S. Hensel, T. Laux, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-09-13T12:17:11Z
date_published: 2021-08-03T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '03'
department:
- _id: JuFi
doi: 10.48550/arXiv.2108.01733
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2108.01733
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: draft
related_material:
record:
- id: '13043'
relation: later_version
status: public
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9039'
abstract:
- lang: eng
text: We give a short and self-contained proof for rates of convergence of the Allen--Cahn
equation towards mean curvature flow, assuming that a classical (smooth) solution
to the latter exists and starting from well-prepared initial data. Our approach
is based on a relative entropy technique. In particular, it does not require a
stability analysis for the linearized Allen--Cahn operator. As our analysis also
does not rely on the comparison principle, we expect it to be applicable to more
complex equations and systems.
acknowledgement: "This work was supported by the European Union's Horizon 2020 Research
and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385
and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation)
under Germany's Excellence Strategy, EXC-2047/1--390685813."
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Theresa M.
full_name: Simon, Theresa M.
last_name: Simon
citation:
ama: 'Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182'
apa: 'Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of
the Allen-Cahn equation to mean curvature flow: A short proof based on relative
entropies. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/20M1322182'
chicago: 'Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates
of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative
Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.'
ieee: 'J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn
equation to mean curvature flow: A short proof based on relative entropies,” SIAM
Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and
Applied Mathematics, pp. 6222–6233, 2020.'
ista: 'Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 52(6), 6222–6233.'
mla: 'Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to
Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal
on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied
Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.'
short: J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis
52 (2020) 6222–6233.
corr_author: '1'
date_created: 2021-01-24T23:01:09Z
date_published: 2020-12-15T00:00:00Z
date_updated: 2025-07-10T12:01:32Z
day: '15'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/20M1322182
ec_funded: 1
external_id:
isi:
- '000600695200027'
file:
- access_level: open_access
checksum: 21aa1cf4c30a86a00cae15a984819b5d
content_type: application/pdf
creator: dernst
date_created: 2021-01-25T07:48:39Z
date_updated: 2021-01-25T07:48:39Z
file_id: '9041'
file_name: 2020_SIAM_Fischer.pdf
file_size: 310655
relation: main_file
success: 1
file_date_updated: 2021-01-25T07:48:39Z
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 6222-6233
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates of the Allen-Cahn equation to mean curvature flow: A short
proof based on relative entropies'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2020'
...
---
_id: '9196'
abstract:
- lang: eng
text: In order to provide a local description of a regular function in a small neighbourhood
of a point x, it is sufficient by Taylor’s theorem to know the value of the function
as well as all of its derivatives up to the required order at the point x itself.
In other words, one could say that a regular function is locally modelled by the
set of polynomials. The theory of regularity structures due to Hairer generalizes
this observation and provides an abstract setup, which in the application to singular
SPDE extends the set of polynomials by functionals constructed from, e.g., white
noise. In this context, the notion of Taylor polynomials is lifted to the notion
of so-called modelled distributions. The celebrated reconstruction theorem, which
in turn was inspired by Gubinelli’s \textit {sewing lemma}, is of paramount importance
for the theory. It enables one to reconstruct a modelled distribution as a true
distribution on Rd which is locally approximated by this extended set of models
or “monomials”. In the original work of Hairer, the error is measured by means
of Hölder norms. This was then generalized to the whole scale of Besov spaces
by Hairer and Labbé. It is the aim of this work to adapt the analytic part of
the theory of regularity structures to the scale of Triebel–Lizorkin spaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tommaso
full_name: Rosati, Tommaso
last_name: Rosati
citation:
ama: Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia
Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2
apa: Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin
type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2
chicago: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2.
ieee: S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,”
Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297,
2020.
ista: Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type.
Studia Mathematica. 252(3), 251–297.
mla: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020,
pp. 251–97, doi:10.4064/sm180411-11-2.
short: S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.
date_created: 2021-02-25T08:55:03Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2025-06-24T12:07:06Z
day: '01'
department:
- _id: JuFi
- _id: GradSch
doi: 10.4064/sm180411-11-2
external_id:
arxiv:
- '1709.05202'
isi:
- '000558100500002'
intvolume: ' 252'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1709.05202
month: '03'
oa: 1
oa_version: Preprint
page: 251-297
publication: Studia Mathematica
publication_identifier:
eissn:
- 1730-6337
issn:
- 0039-3223
publication_status: published
publisher: Instytut Matematyczny
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modelled distributions of Triebel–Lizorkin type
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 252
year: '2020'
...
---
_id: '7637'
abstract:
- lang: eng
text: The evolution of finitely many particles obeying Langevin dynamics is described
by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz
multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki
model based on second order Langevin dynamics by analysing a system of particles
interacting via a pairwise potential. Key tools of our analysis are the propagation
of chaos and Simon's compactness criterion. The model we obtain is a small-noise
stochastic perturbation of the undamped McKean–Vlasov equation. We also provide
a high-probability result for existence and uniqueness for our model.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised
Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting
particles to a regularised Dean-Kawasaki model. Nonlinearity. IOP Publishing.
https://doi.org/10.1088/1361-6544/ab5174
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting
Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity. IOP Publishing,
2020. https://doi.org/10.1088/1361-6544/ab5174.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles
to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2. IOP
Publishing, pp. 864–891, 2020.
ista: Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles
to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.
mla: Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised
Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020,
pp. 864–91, doi:10.1088/1361-6544/ab5174.
short: F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.
date_created: 2020-04-05T22:00:49Z
date_published: 2020-01-10T00:00:00Z
date_updated: 2026-04-02T14:26:08Z
day: '10'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab5174
external_id:
arxiv:
- '1811.06448'
isi:
- '000508175400001'
intvolume: ' 33'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.06448
month: '01'
oa: 1
oa_version: Preprint
page: 864-891
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: From weakly interacting particles to a regularised Dean-Kawasaki model
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 33
year: '2020'
...
---
_id: '8697'
abstract:
- lang: eng
text: In the computation of the material properties of random alloys, the method
of 'special quasirandom structures' attempts to approximate the properties of
the alloy on a finite volume with higher accuracy by replicating certain statistics
of the random atomic lattice in the finite volume as accurately as possible. In
the present work, we provide a rigorous justification for a variant of this method
in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach
is based on a recent analysis of a related variance reduction method in stochastic
homogenization of linear elliptic PDEs and the locality properties of the TFW
model. Concerning the latter, we extend an exponential locality result by Nazar
and Ortner to include point charges, a result that may be of independent interest.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices
in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772.
doi:10.1088/1361-6544/ab9728
apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies
of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity.
IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728
chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective
Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity.
IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.
ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of
random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity,
vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.
ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random
lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.
mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies
of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity,
vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.
short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.
corr_author: '1'
date_created: 2020-10-25T23:01:16Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2026-04-02T14:31:34Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab9728
external_id:
arxiv:
- '1906.12245'
isi:
- '000576492700001'
file:
- access_level: open_access
checksum: ed90bc6eb5f32ee6157fef7f3aabc057
content_type: application/pdf
creator: cziletti
date_created: 2020-10-27T12:09:57Z
date_updated: 2020-10-27T12:09:57Z
file_id: '8710'
file_name: 2020_Nonlinearity_Fischer.pdf
file_size: 1223899
relation: main_file
success: 1
file_date_updated: 2020-10-27T12:09:57Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
issue: '11'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '11'
oa: 1
oa_version: Published Version
page: 5733-5772
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von
Weizsäcker model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 33
year: '2020'
...
---
_id: '7489'
abstract:
- lang: eng
text: 'In the present work, we consider the evolution of two fluids separated by
a sharp interface in the presence of surface tension—like, for example, the evolution
of oil bubbles in water. Our main result is a weak–strong uniqueness principle
for the corresponding free boundary problem for the incompressible Navier–Stokes
equation: as long as a strong solution exists, any varifold solution must coincide
with it. In particular, in the absence of physical singularities, the concept
of varifold solutions—whose global in time existence has been shown by Abels (Interfaces
Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism
for non-uniqueness. The key ingredient of our approach is the construction of
a relative entropy functional capable of controlling the interface error. If the
viscosities of the two fluids do not coincide, even for classical (strong) solutions
the gradient of the velocity field becomes discontinuous at the interface, introducing
the need for a careful additional adaption of the relative entropy.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
2020;236:967-1087. doi:10.1007/s00205-019-01486-2
apa: Fischer, J. L., & Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension. Archive for Rational Mechanics
and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01486-2
chicago: Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Surface Tension.” Archive for Rational
Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-019-01486-2.
ieee: J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes
equation for two fluids with surface tension,” Archive for Rational Mechanics
and Analysis, vol. 236. Springer Nature, pp. 967–1087, 2020.
ista: Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation
for two fluids with surface tension. Archive for Rational Mechanics and Analysis.
236, 967–1087.
mla: Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Surface Tension.” Archive for Rational Mechanics
and Analysis, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:10.1007/s00205-019-01486-2.
short: J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236
(2020) 967–1087.
corr_author: '1'
date_created: 2020-02-16T23:00:50Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '01'
ddc:
- '530'
- '532'
department:
- _id: JuFi
doi: 10.1007/s00205-019-01486-2
ec_funded: 1
external_id:
isi:
- '000511060200001'
file:
- access_level: open_access
checksum: f107e21b58f5930876f47144be37cf6c
content_type: application/pdf
creator: dernst
date_created: 2020-11-20T09:14:22Z
date_updated: 2020-11-20T09:14:22Z
file_id: '8779'
file_name: 2020_ArchRatMechAn_Fischer.pdf
file_size: 1897571
relation: main_file
success: 1
file_date_updated: 2020-11-20T09:14:22Z
has_accepted_license: '1'
intvolume: ' 236'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 967-1087
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '10007'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface
tension
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 236
year: '2020'
...
---
_id: '10012'
abstract:
- lang: eng
text: We prove that in the absence of topological changes, the notion of BV solutions
to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical)
non-uniqueness. Our approach is based on the local structure of the energy landscape
near a classical evolution by mean curvature. Mean curvature flow being the gradient
flow of the surface energy functional, we develop a gradient-flow analogue of
the notion of calibrations. Just like the existence of a calibration guarantees
that one has reached a global minimum in the energy landscape, the existence of
a "gradient flow calibration" ensures that the route of steepest descent in the
energy landscape is unique and stable.
acknowledgement: Parts of the paper were written during the visit of the authors to
the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the
framework of the trimester program “Evolution of Interfaces”. The support and the
hospitality of HIM are gratefully acknowledged. This project has received funding
from the European Union’s Horizon 2020 research and innovation programme under the
Marie Sklodowska-Curie Grant Agreement No. 665385.
article_number: '2003.05478'
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Thilo
full_name: Simon, Thilo
last_name: Simon
citation:
ama: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape
in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions.
arXiv. doi:10.48550/arXiv.2003.05478'
apa: 'Fischer, J. L., Hensel, S., Laux, T., & Simon, T. (n.d.). The local structure
of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions. arXiv. https://doi.org/10.48550/arXiv.2003.05478'
chicago: 'Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local
Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong
Uniqueness and Stability of Evolutions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2003.05478.'
ieee: 'J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of
the energy landscape in multiphase mean curvature flow: weak-strong uniqueness
and stability of evolutions,” arXiv. .'
ista: 'Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy
landscape in multiphase mean curvature flow: weak-strong uniqueness and stability
of evolutions. arXiv, 2003.05478.'
mla: 'Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in
Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.”
ArXiv, 2003.05478, doi:10.48550/arXiv.2003.05478.'
short: J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).
date_created: 2021-09-13T12:17:11Z
date_published: 2020-03-11T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '11'
department:
- _id: JuFi
doi: 10.48550/arXiv.2003.05478
ec_funded: 1
external_id:
arxiv:
- '2003.05478'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.05478
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: arXiv
publication_status: draft
related_material:
record:
- id: '10007'
relation: dissertation_contains
status: public
status: public
title: 'The local structure of the energy landscape in multiphase mean curvature flow:
weak-strong uniqueness and stability of evolutions'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2020'
...
---
_id: '7866'
abstract:
- lang: eng
text: In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination
system modelling the charge transport within certain semiconductor devices. More
precisely, we consider a two-level system for electrons and holes which is augmented
by an intermediate energy level for electrons in so-called trapped states. The
recombination dynamics use the mass action principle by taking into account this
additional trap level. The main part of the paper is concerned with the derivation
of an entropy–entropy production inequality, which entails exponential convergence
to the equilibrium via the so-called entropy method. The novelty of our approach
lies in the fact that the entropy method is applied uniformly in a fast-reaction
parameter which governs the lifetime of electrons on the trap level. Thus, the
resulting decay estimate for the densities of electrons and holes extends to the
corresponding quasi-steady-state approximation.
acknowledgement: Open access funding provided by Austrian Science Fund (FWF). The
second author has been supported by the International Research Training Group IGDK
1754 “Optimization and Numerical Analysis for Partial Differential Equations with
Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian
Science Fund (FWF) under grant number [W 1244-N18].
article_processing_charge: No
article_type: original
author:
- first_name: Klemens
full_name: Fellner, Klemens
last_name: Fellner
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion
models with trap-assisted recombination and the limiting Shockley–Read–Hall model.
Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8
apa: Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for
a family of drift–diffusion models with trap-assisted recombination and the limiting
Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations.
Springer Nature. https://doi.org/10.1007/s41808-020-00068-8
chicago: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium
for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the
Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations.
Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8.
ieee: K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family
of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall
model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature,
pp. 529–598, 2020.
ista: Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family
of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall
model. Journal of Elliptic and Parabolic Equations. 6, 529–598.
mla: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for
a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting
Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations,
vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8.
short: K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020)
529–598.
corr_author: '1'
date_created: 2020-05-17T22:00:45Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2025-07-17T08:12:24Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s41808-020-00068-8
external_id:
pmid:
- '33195442'
file:
- access_level: open_access
checksum: 6bc6832caacddceee1471291e93dcf1d
content_type: application/pdf
creator: dernst
date_created: 2020-11-25T08:59:59Z
date_updated: 2020-11-25T08:59:59Z
file_id: '8802'
file_name: 2020_JourEllipticParabEquat_Fellner.pdf
file_size: 8408694
relation: main_file
success: 1
file_date_updated: 2020-11-25T08:59:59Z
has_accepted_license: '1'
intvolume: ' 6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 529-598
pmid: 1
project:
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
eissn:
- 2296-9039
issn:
- 2296-9020
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Uniform convergence to equilibrium for a family of drift–diffusion models with
trap-assisted recombination and the limiting Shockley–Read–Hall model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2020'
...
---
_id: '151'
abstract:
- lang: eng
text: We construct planar bi-Sobolev mappings whose local volume distortion is bounded
from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2
we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞,
we provide bi-Lipschitz maps. The basic building block of our construction are
bi-Lipschitz maps which stretch a given compact subset of the unit square by a
given factor while preserving the boundary. The construction of these stretching
maps relies on a slight strengthening of the celebrated covering result of Alberti,
Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We
apply our result to a model functional in nonlinear elasticity, the integrand
of which features fast blowup as the Jacobian determinant of the deformation becomes
small. For such functionals, the derivation of the equilibrium equations for minimizers
requires an additional regularization of test functions, which our maps provide.
article_processing_charge: No
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Olivier
full_name: Kneuss, Olivier
last_name: Kneuss
citation:
ama: Fischer JL, Kneuss O. Bi-Sobolev solutions to the prescribed Jacobian inequality
in the plane with L p data and applications to nonlinear elasticity. Journal
of Differential Equations. 2019;266(1):257-311. doi:10.1016/j.jde.2018.07.045
apa: Fischer, J. L., & Kneuss, O. (2019). Bi-Sobolev solutions to the prescribed
Jacobian inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2018.07.045
chicago: Fischer, Julian L, and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations. Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.07.045.
ieee: J. L. Fischer and O. Kneuss, “Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity,”
Journal of Differential Equations, vol. 266, no. 1. Elsevier, pp. 257–311,
2019.
ista: Fischer JL, Kneuss O. 2019. Bi-Sobolev solutions to the prescribed Jacobian
inequality in the plane with L p data and applications to nonlinear elasticity.
Journal of Differential Equations. 266(1), 257–311.
mla: Fischer, Julian L., and Olivier Kneuss. “Bi-Sobolev Solutions to the Prescribed
Jacobian Inequality in the Plane with L p Data and Applications to Nonlinear Elasticity.”
Journal of Differential Equations, vol. 266, no. 1, Elsevier, 2019, pp.
257–311, doi:10.1016/j.jde.2018.07.045.
short: J.L. Fischer, O. Kneuss, Journal of Differential Equations 266 (2019) 257–311.
date_created: 2018-12-11T11:44:54Z
date_published: 2019-01-05T00:00:00Z
date_updated: 2023-09-08T13:25:35Z
day: '05'
department:
- _id: JuFi
doi: 10.1016/j.jde.2018.07.045
external_id:
arxiv:
- '1408.1587'
isi:
- '000449108500010'
intvolume: ' 266'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.1587
month: '01'
oa: 1
oa_version: Preprint
page: 257 - 311
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
publist_id: '7770'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with
L p data and applications to nonlinear elasticity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 266
year: '2019'
...