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arXiv · 1912.08667

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

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 $\mathcal H^s$, $s>\frac45$.

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Leonardo Tolomeo. 2019-12-18. Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain. https://doi.org/10.1214/20-aop1484

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