Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

Ruoyuan Liu

Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

Analysis of PDEs 2023-04-06 v2 Probability

Authors: Ruoyuan Liu

Abstract

We study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove pathwise global well-posedness of the stochastic defocusing vNLW with an additive stochastic forcing $D^\alpha \xi$ , where $\alpha < \frac 12$ and $\xi$ denotes the space-time white noise.

Keywords

viscous nonlinear wave equation stochastic forcing global well-posedness two-dimensional torus space-time white noise

Cite

@article{arxiv.2203.15393,
  title  = {Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations},
  author = {Ruoyuan Liu},
  journal= {arXiv preprint arXiv:2203.15393},
  year   = {2023}
}

Comments

28 pages. The case of randomized initial data is moved to Remark 1.4 (iii). To appear in Stoch. Partial Differ. Equ. Anal. Comput

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