Renormalization of the two-dimensional stochastic nonlinear wave equations

Tadahiro Oh; Massimilano Gubinelli; Herbert Koch

doi:10.1090/tran/7452

Renormalization of the two-dimensional stochastic nonlinear wave equations

Tadahiro Oh, Massimilano Gubinelli, Herbert Koch

School of Mathematics

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

Abstract

We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renor- malization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.

Original language	English
Pages (from-to)	7335-7359
Number of pages	25
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	10
Early online date	7 Jun 2018
DOIs	https://doi.org/10.1090/tran/7452
Publication status	Published - Oct 2018

Keywords / Materials (for Non-textual outputs)

stochastic nonlinear wave equation
nonlinear wave equation
renormalization
Wick ordering
Hermite polynomial
white noise

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10.1090/tran/7452

1703.05461
First published in Transactions of the AMS in 2017, published by the American Mathematical Society
Accepted author manuscript, 339 KBLicence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

https://arxiv.org/abs/1703.05461

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

Cite this

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title = "Renormalization of the two-dimensional stochastic nonlinear wave equations",

abstract = "We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renor- malization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.",

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AU - Gubinelli, Massimilano

AU - Koch, Herbert

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N2 - We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renor- malization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.

AB - We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renor- malization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.

KW - stochastic nonlinear wave equation

KW - nonlinear wave equation

KW - renormalization

KW - Wick ordering

KW - Hermite polynomial

KW - white noise

U2 - 10.1090/tran/7452

DO - 10.1090/tran/7452

M3 - Article

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VL - 370

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 10

ER -

Renormalization of the two-dimensional stochastic nonlinear wave equations

Abstract

Keywords / Materials (for Non-textual outputs)

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this