---
OA_place: repository
OA_type: green
_id: '22025'
abstract:
- lang: eng
  text: We consider the mass-subcritical nonlinear Schr¨odinger equation in all space
    dimensions with focusing or defocusing nonlinearity. For such equations with critical
    regularity sc ∈ (max{−1, −d/2 }, 0), we prove that any solution satisfying {mathematical
    formular} on its maximal interval of existence must be global and scatter.
article_number: '38'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Satoshi
  full_name: Masaki, Satoshi
  last_name: Masaki
- first_name: Jason
  full_name: Murphy, Jason
  last_name: Murphy
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Killip R, Masaki S, Murphy J, Vişan M. Large data mass-subcritical NLS: Critical
    weighted bounds imply scattering. <i>Nonlinear Differential Equations and Applications
    NoDEA</i>. 2017;24(4). doi:<a href="https://doi.org/10.1007/s00030-017-0463-9">10.1007/s00030-017-0463-9</a>'
  apa: 'Killip, R., Masaki, S., Murphy, J., &#38; Vişan, M. (2017). Large data mass-subcritical
    NLS: Critical weighted bounds imply scattering. <i>Nonlinear Differential Equations
    and Applications NoDEA</i>. Springer Nature. <a href="https://doi.org/10.1007/s00030-017-0463-9">https://doi.org/10.1007/s00030-017-0463-9</a>'
  chicago: 'Killip, Rowan, Satoshi Masaki, Jason Murphy, and Monica Vişan. “Large
    Data Mass-Subcritical NLS: Critical Weighted Bounds Imply Scattering.” <i>Nonlinear
    Differential Equations and Applications NoDEA</i>. Springer Nature, 2017. <a href="https://doi.org/10.1007/s00030-017-0463-9">https://doi.org/10.1007/s00030-017-0463-9</a>.'
  ieee: 'R. Killip, S. Masaki, J. Murphy, and M. Vişan, “Large data mass-subcritical
    NLS: Critical weighted bounds imply scattering,” <i>Nonlinear Differential Equations
    and Applications NoDEA</i>, vol. 24, no. 4. Springer Nature, 2017.'
  ista: 'Killip R, Masaki S, Murphy J, Vişan M. 2017. Large data mass-subcritical
    NLS: Critical weighted bounds imply scattering. Nonlinear Differential Equations
    and Applications NoDEA. 24(4), 38.'
  mla: 'Killip, Rowan, et al. “Large Data Mass-Subcritical NLS: Critical Weighted
    Bounds Imply Scattering.” <i>Nonlinear Differential Equations and Applications
    NoDEA</i>, vol. 24, no. 4, 38, Springer Nature, 2017, doi:<a href="https://doi.org/10.1007/s00030-017-0463-9">10.1007/s00030-017-0463-9</a>.'
  short: R. Killip, S. Masaki, J. Murphy, M. Vişan, Nonlinear Differential Equations
    and Applications NoDEA 24 (2017).
das_tickbox: '1'
date_created: 2026-06-19T07:32:33Z
date_published: 2017-06-15T00:00:00Z
date_updated: 2026-06-22T10:26:09Z
day: '15'
doi: 10.1007/s00030-017-0463-9
extern: '1'
external_id:
  arxiv:
  - '1606.01512'
fulldoi: https://doi.org/10.1007/s00030-017-0463-9
intvolume: '        24'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1606.01512
month: '06'
oa: 1
oa_version: Preprint
publication: Nonlinear Differential Equations and Applications NoDEA
publication_identifier:
  eissn:
  - 1420-9004
  issn:
  - 1021-9722
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Large data mass-subcritical NLS: Critical weighted bounds imply scattering'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2017'
...
---
OA_type: closed access
_id: '1309'
abstract:
- lang: eng
  text: We show that weak solutions of the Derrida-Lebowitz-Speer-Spohn (DLSS) equation
    display infinite speed of support propagation. We apply our method to the case
    of the quantum drift-diffusion equation which augments the DLSS equation with
    a drift term and possibly a second-order diffusion term. The proof is accomplished
    using weighted entropy estimates, Hardy's inequality and a family of singular
    weight functions to derive a differential inequality; the differential inequality
    shows exponential growth of the weighted entropy, with the growth constant blowing
    up very fast as the singularity of the weight becomes sharper. To the best of
    our knowledge, this is the first example of a nonnegativity-preserving higher-order
    parabolic equation displaying infinite speed of support propagation.
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
citation:
  ama: Fischer JL. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
    equation and quantum drift-diffusion models. <i>Nonlinear Differential Equations
    and Applications</i>. 2014;21(1):27-50. doi:<a href="https://doi.org/10.1007/s00030-013-0235-0">10.1007/s00030-013-0235-0</a>
  apa: Fischer, J. L. (2014). Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
    equation and quantum drift-diffusion models. <i>Nonlinear Differential Equations
    and Applications</i>. Birkhäuser. <a href="https://doi.org/10.1007/s00030-013-0235-0">https://doi.org/10.1007/s00030-013-0235-0</a>
  chicago: Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn
    Equation and Quantum Drift-Diffusion Models.” <i>Nonlinear Differential Equations
    and Applications</i>. Birkhäuser, 2014. <a href="https://doi.org/10.1007/s00030-013-0235-0">https://doi.org/10.1007/s00030-013-0235-0</a>.
  ieee: J. L. Fischer, “Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
    equation and quantum drift-diffusion models,” <i>Nonlinear Differential Equations
    and Applications</i>, vol. 21, no. 1. Birkhäuser, pp. 27–50, 2014.
  ista: Fischer JL. 2014. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
    equation and quantum drift-diffusion models. Nonlinear Differential Equations
    and Applications. 21(1), 27–50.
  mla: Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn
    Equation and Quantum Drift-Diffusion Models.” <i>Nonlinear Differential Equations
    and Applications</i>, vol. 21, no. 1, Birkhäuser, 2014, pp. 27–50, doi:<a href="https://doi.org/10.1007/s00030-013-0235-0">10.1007/s00030-013-0235-0</a>.
  short: J.L. Fischer, Nonlinear Differential Equations and Applications 21 (2014)
    27–50.
date_created: 2018-12-11T11:51:17Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2026-09-04T11:56:53Z
day: '01'
doi: 10.1007/s00030-013-0235-0
extern: '1'
fulldoi: https://doi.org/10.1007/s00030-013-0235-0
intvolume: '        21'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 27 - 50
publication: Nonlinear Differential Equations and Applications
publication_identifier:
  eissn:
  - 1420-9004
  issn:
  - 1021-9722
publication_status: published
publisher: Birkhäuser
publist_id: '5960'
status: public
title: Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
  equation and quantum drift-diffusion models
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 21
year: '2014'
...