Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain

Leonardo Tolomeo

doi:10.1214/20-AOP1484

Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain

Analysis of PDEs 2021-09-07 v1 Probability

Authors: Leonardo Tolomeo

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Abstract

We study the two-dimensional wave equation with cubic nonlinearity posed on $\mathbb R^2$ , with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for initial data in $\mathcal H^s$ , $s>\frac45$ .

Keywords

stochastic wave equation global well-posedness cubic nonlinearity space-time white noise renormalization unbounded domain

Cite

@article{arxiv.1912.08667,
  title  = {Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain},
  author = {Leonardo Tolomeo},
  journal= {arXiv preprint arXiv:1912.08667},
  year   = {2021}
}

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23 pages, 0 figures

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