Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise

Tadahiro Oh, Yuzhao Wang, Younes Zine

Research output: Contribution to journalArticlepeer-review

Abstract

We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus 𝕋^3. In particular, we prove local well-posedness of the (renormalized) SNLW when the noise is almost a space-time white noise. In recent years, the paracontrolled calculus has played a crucial role in the well-posedness study of singular SNLW on 𝕋^3 by Gubinelli, Koch, and the first author (2018), Okamoto, Tolomeo, and the first author (2020), and Bringmann (2020). Our approach, however, does not rely on the paracontrolled calculus. We instead proceed with the second order expansion and study the resulting equation for the residual term, using multilinear dispersive smoothing.
Original languageEnglish
Number of pages66
JournalStochastics and Partial Differential Equations: Analysis and Computations
Early online date13 Apr 2022
DOIs
Publication statusE-pub ahead of print - 13 Apr 2022

Keywords

  • stochastic nonlinear wave equation
  • nonlinear wave equation

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