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arXiv · 1903.04441

New examples of probabilistic well-posedness for nonlinear wave equations

Chenmin Sun·Nikolay Tzvetkov
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Abstract

We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures. We provide ill-posedness constructions showing that the results are truly super-critical in the considered functional setting. We also present a result in the case of a general randomisation in the spirit of the work by N. Burq and the second author.

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Chenmin Sun, Nikolay Tzvetkov. 2019-03-11. New examples of probabilistic well-posedness for nonlinear wave equations. https://arxiv.org/abs/1903.04441

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