---
_id: '11858'
abstract:
- lang: eng
text: "This paper is a continuation of Part I of this project, where we developed
a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian
noise. In the current Part II we consider blow-up criteria and regularization
phenomena. As in Part I we can allow nonlinearities with polynomial growth and
rough initial values from critical spaces. In the first main result we obtain
several new blow-up criteria for quasi- and semilinear stochastic evolution equations.
In particular, for semilinear equations we obtain a Serrin type blow-up criterium,
which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074,
2018) to the stochastic setting. Blow-up criteria can be used to prove global
well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights
in time play a central role in the proofs. Our second contribution is a new method
to bootstrap Sobolev and Hölder regularity in time and space, which does not require
smoothness of the initial data. The blow-up criteria are at the basis of these
new methods. Moreover, in applications the bootstrap results can be combined with
our blow-up criteria, to obtain efficient ways to prove global existence. This
gives new results even in classical \U0001D43F2-settings, which we illustrate
for a concrete SPDE. In future works in preparation we apply the results of the
current paper to obtain global well-posedness results and regularity for several
concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion
equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into
a more flexible framework, where less restrictions on the nonlinearities are needed,
and we are able to treat rough initial values from critical spaces. Moreover,
we will obtain higher-order regularity results."
acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors
thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '56'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in
critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces part II. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00786-7
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations.
Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces part II,” Journal of Evolution Equations, vol. 22, no.
2. Springer Nature, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces part II. Journal of Evolution Equations. 22(2), 56.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations,
vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7.
short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).
corr_author: '1'
date_created: 2022-08-16T08:39:43Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2024-10-09T21:03:06Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00028-022-00786-7
external_id:
isi:
- '000809108500001'
file:
- access_level: open_access
checksum: 59b99d1b48b6bd40983e7ce298524a21
content_type: application/pdf
creator: kschuh
date_created: 2022-08-16T08:52:46Z
date_updated: 2022-08-16T08:52:46Z
file_id: '11862'
file_name: 2022_Journal of Evolution Equations_Agresti.pdf
file_size: 1758371
relation: main_file
success: 1
file_date_updated: 2022-08-16T08:52:46Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces part
II
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: 22
year: '2022'
...
---
_id: '12145'
abstract:
- lang: eng
text: In the class of strictly convex smooth boundaries each of which has no strip
around its boundary foliated by invariant curves, we prove that the Taylor coefficients
of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In
contrast, we prove that any two elliptic billiard maps are C0-conjugate near their
respective boundaries, and C∞-conjugate, near the boundary and away from a line
passing through the center of the underlying ellipse. We also prove that, if the
billiard maps corresponding to two ellipses are topologically conjugate, then
the two ellipses are similar.
acknowledgement: "We are grateful to the anonymous referees for their careful reading
and valuable remarks and\r\ncomments which helped to improve the paper significantly.
We gratefully acknowledge support from the European Research Council (ERC) through
the Advanced Grant “SPERIG” (#885707)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy.
Regular and Chaotic Dynamics. 2022;27(6):525-537. doi:10.1134/S1560354722050021
apa: Koudjinan, E., & Kaloshin, V. (2022). On some invariants of Birkhoff billiards
under conjugacy. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354722050021
chicago: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff
Billiards under Conjugacy.” Regular and Chaotic Dynamics. Springer Nature,
2022. https://doi.org/10.1134/S1560354722050021.
ieee: E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under
conjugacy,” Regular and Chaotic Dynamics, vol. 27, no. 6. Springer Nature,
pp. 525–537, 2022.
ista: Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under
conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.
mla: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards
under Conjugacy.” Regular and Chaotic Dynamics, vol. 27, no. 6, Springer
Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021.
short: E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537.
corr_author: '1'
date_created: 2023-01-12T12:06:49Z
date_published: 2022-10-03T00:00:00Z
date_updated: 2025-04-14T07:53:45Z
day: '03'
department:
- _id: VaKa
doi: 10.1134/S1560354722050021
ec_funded: 1
external_id:
arxiv:
- '2105.14640'
isi:
- '000865267300002'
intvolume: ' 27'
isi: 1
issue: '6'
keyword:
- Mechanical Engineering
- Applied Mathematics
- Mathematical Physics
- Modeling and Simulation
- Statistical and Nonlinear Physics
- Mathematics (miscellaneous)
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.14640
month: '10'
oa: 1
oa_version: Preprint
page: 525-537
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Regular and Chaotic Dynamics
publication_identifier:
eissn:
- 1468-4845
issn:
- 1560-3547
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1134/s1560354722060107
scopus_import: '1'
status: public
title: On some invariants of Birkhoff billiards under conjugacy
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2022'
...
---
_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: '8418'
abstract:
- lang: eng
text: For the Restricted Circular Planar 3 Body Problem, we show that there exists
an open set U in phase space of fixed measure, where the set of initial points
which lead to collision is O(μ120) dense as μ→0.
article_processing_charge: No
article_type: original
author:
- first_name: Marcel
full_name: Guardia, Marcel
last_name: Guardia
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Jianlu
full_name: Zhang, Jianlu
last_name: Zhang
citation:
ama: Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the
Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and
Analysis. 2019;233(2):799-836. doi:10.1007/s00205-019-01368-7
apa: Guardia, M., Kaloshin, V., & Zhang, J. (2019). Asymptotic density of collision
orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01368-7
chicago: Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density
of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2019. https://doi.org/10.1007/s00205-019-01368-7.
ieee: M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits
in the Restricted Circular Planar 3 Body Problem,” Archive for Rational Mechanics
and Analysis, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.
ista: Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits
in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics
and Analysis. 233(2), 799–836.
mla: Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted
Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis,
vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:10.1007/s00205-019-01368-7.
short: M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis
233 (2019) 799–836.
date_created: 2020-09-17T10:41:51Z
date_published: 2019-03-12T00:00:00Z
date_updated: 2021-01-12T08:19:09Z
day: '12'
doi: 10.1007/s00205-019-01368-7
extern: '1'
intvolume: ' 233'
issue: '2'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00205-019-01368-7
month: '03'
oa: 1
oa_version: Published Version
page: 799-836
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
issn:
- 0003-9527
- 1432-0673
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Asymptotic density of collision orbits in the Restricted Circular Planar 3
Body Problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 233
year: '2019'
...
---
_id: '8508'
abstract:
- lang: eng
text: We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving
diffeomorphisms (conservative New house phenomena) and show that they give rise
to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications,
we discuss the size of the stochastic layer of a standard map and the Hausdorff
dimension of invariant hyperbolic sets for certain restricted three-body problems.
We avoid involved technical details and only concentrate on the ideas of the proof
of the presented results.
article_processing_charge: No
article_type: original
author:
- first_name: Anton
full_name: Gorodetski, Anton
last_name: Gorodetski
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications.
Proceedings of the Steklov Institute of Mathematics. 2009;267(1):76-90.
doi:10.1134/s0081543809040063
apa: Gorodetski, A., & Kaloshin, V. (2009). Conservative homoclinic bifurcations
and some applications. Proceedings of the Steklov Institute of Mathematics.
Springer Nature. https://doi.org/10.1134/s0081543809040063
chicago: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations
and Some Applications.” Proceedings of the Steklov Institute of Mathematics.
Springer Nature, 2009. https://doi.org/10.1134/s0081543809040063.
ieee: A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some
applications,” Proceedings of the Steklov Institute of Mathematics, vol.
267, no. 1. Springer Nature, pp. 76–90, 2009.
ista: Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some
applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.
mla: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations
and Some Applications.” Proceedings of the Steklov Institute of Mathematics,
vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:10.1134/s0081543809040063.
short: A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics
267 (2009) 76–90.
date_created: 2020-09-18T10:48:03Z
date_published: 2009-12-01T00:00:00Z
date_updated: 2021-01-12T08:19:46Z
day: '01'
doi: 10.1134/s0081543809040063
extern: '1'
intvolume: ' 267'
issue: '1'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '12'
oa_version: None
page: 76-90
publication: Proceedings of the Steklov Institute of Mathematics
publication_identifier:
issn:
- 0081-5438
- 1531-8605
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Conservative homoclinic bifurcations and some applications
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2009'
...