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

Ruoyuan Liu

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arXiv · 2203.15393

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

Ruoyuan Liu

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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 $D^αξ$, where $α< \frac 12$ and $ξ$ denotes the space-time white noise.

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Ruoyuan Liu. 2023-04-04. Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations. https://arxiv.org/abs/2203.15393

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