On the two-dimensional singular stochastic viscous nonlinear wave equations

Ruoyuan Liu, Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We study the stochastic viscous nonlinear wave equations (SvNLW) on T^2, forced by a fractional derivative of the space-time white noise ξ. In particular, we consider SvNLW with the singular additive forcing D^{1/2}ξ such that solutions are expected to be merely distributions. By introducing an appropriate renormalization, we prove local well-posedness of SvNLW. By establishing an energy bound via a Yudovich-type argument, we also prove pathwise global well-posedness of the defocusing cubic SvNLW. Lastly, in = the defocusing case, we prove almost sure global well-posedness
of SvNLW with respect to certain Gaussian random initial data.
Original languageEnglish
Pages (from-to)1227-1248
Number of pages22
JournalComptes Rendus Mathématique
Publication statusPublished - 8 Dec 2022

Keywords / Materials (for Non-textual outputs)

  • stochastic viscous nonlinear wave equation
  • viscous nonlinear wave equation
  • Gibbs measure


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