Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation

被引：12
|
作者：
Oh, Tadahiro [1 ,2 ]
Tzvetkov, Nikolay [3 ]
机构：
[1] Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland
[2] James Clerk Maxwell Bldg, Maxwell Inst Math Sci, Kings Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland
[3] Univ Cergy Pontoise, 2 Av Adolphe Chauvin, F-95302 Cergy Pontoise, France
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2020年 / 22卷 / 06期
基金：
欧洲研究理事会;
关键词：
Nonlinear wave equation; nonlinear Klein-Gordon equation; Gaussian measure; quasi-invariance; WIENER SPACE; DIFFERENTIAL-EQUATIONS;
D O I：
10.4171/JEMS/956
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the two-dimensional defocusing cubic nonlinear wave equation (NLW). Under some regularity condition, we prove quasi-invariance of the mean-zero Gaussian measures on Sobolev spaces for the NLW dynamics. We achieve this by introducing a simultaneous renormalization of the energy functional and its time derivative and establishing a renormalized energy estimate in the probabilistic setting.
引用
收藏
页码：1785 / 1826
页数：42
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