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New examples of probabilistic well-posedness for nonlinear wave equations

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arxiv 1903.04441 v2 pith:QYUVHY3M submitted 2019-03-11 math.AP

New examples of probabilistic well-posedness for nonlinear wave equations

classification math.AP
keywords equationswavewell-posednessarbitraryauthorburqcaseconsider
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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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