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

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arxiv 1912.08667 v1 pith:FZ2SWKVG submitted 2019-12-18 math.AP math.PR

Leonardo Tolomeo This is my paper · ORCID
classification math.APmath.PR
keywords equationglobalnonlinearitytwo-dimensionalwavewell-posednesscubicdata
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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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  1. Comparing the stochastic nonlinear wave and heat equations: a case study

    math.AP 2019-08 accept novelty 7.0 of 10

    For the quadratic stochastic nonlinear wave and heat equations on the two-dimensional torus, standard Da Prato-Debussche solution theory fails at noise roughness alpha = 1/2 (wave) and alpha = 1 (heat), before the sca...

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