Global well-posedness of the energy-critical stochastic nonlinear wave equations

Enguerrand Brun; Guopeng Li; Ruoyuan Liu

doi:10.1016/j.jde.2024.03.032

Global well-posedness of the energy-critical stochastic nonlinear wave equations

Enguerrand Brun
, Guopeng Li^*
, Ruoyuan Liu

^*Corresponding author for this work

École normale supérieure de Lyon
The University of Edinburgh and The Maxwell Institute for the Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on R^d and T^d with d≥3. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by Bényi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on T^d, we prove global well-posedness with the stochastic forcing below the energy space.

Original language	English
Pages (from-to)	316-348
Number of pages	33
Journal	Journal of Differential Equations
Volume	397
DOIs	https://doi.org/10.1016/j.jde.2024.03.032
Publication status	Published - 15 Jul 2024
Externally published	Yes

Keywords

Energy-critical
Global well-posedness
Perturbation theory
Stochastic nonlinear wave equation

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10.1016/j.jde.2024.03.032

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title = "Global well-posedness of the energy-critical stochastic nonlinear wave equations",

abstract = "We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on Rd and Td with d≥3. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by B{\'e}nyi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on Td, we prove global well-posedness with the stochastic forcing below the energy space.",

keywords = "Energy-critical, Global well-posedness, Perturbation theory, Stochastic nonlinear wave equation",

author = "Enguerrand Brun and Guopeng Li and Ruoyuan Liu",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

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doi = "10.1016/j.jde.2024.03.032",

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T1 - Global well-posedness of the energy-critical stochastic nonlinear wave equations

AU - Brun, Enguerrand

AU - Li, Guopeng

AU - Liu, Ruoyuan

PY - 2024/7/15

Y1 - 2024/7/15

N2 - We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on Rd and Td with d≥3. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by Bényi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on Td, we prove global well-posedness with the stochastic forcing below the energy space.

AB - We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on Rd and Td with d≥3. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by Bényi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on Td, we prove global well-posedness with the stochastic forcing below the energy space.

KW - Energy-critical

KW - Global well-posedness

KW - Perturbation theory

KW - Stochastic nonlinear wave equation

UR - https://www.scopus.com/pages/publications/85189953756

U2 - 10.1016/j.jde.2024.03.032

DO - 10.1016/j.jde.2024.03.032

M3 - Article

AN - SCOPUS:85189953756

SN - 0022-0396

VL - 397

SP - 316

EP - 348

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Global well-posedness of the energy-critical stochastic nonlinear wave equations

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Keywords

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