New examples of probabilistic well-posedness for nonlinear wave equations

被引：8

作者：

Sun, Chenmin ^{[1
]}

Tzvetkov, Nikolay ^{[1
]}

机构：

[1] Univ Cergy Pontoise, CNRS, UMR 8088, F-95000 Cergy Pontoise, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 278卷 / 02期

关键词：

Wave equations; Gibbs measure; Uniqueness; Exponential nonlinearities; SCHRODINGER-EQUATION; INVARIANT-MEASURES; REGULARITY; KDV;

D O I：

10.1016/j.jfa.2019.108322

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：47

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