New examples of probabilistic well-posedness for nonlinear wave equations

2019/03/11 by Chenmin Sun, Nikolay Tzvetkov, Sun, Chenmin +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.04441

openalex publication_date 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The spectral function of an elliptic operator

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