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
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.
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页数:47
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