ON THE UNIQUE ERGODICITY FOR A CLASS OF 2 DIMENSIONAL STOCHASTIC WAVE EQUATIONS

被引：1

作者：

Forlano, Justin ^{[1
,2
]}

Tolomeo, Leonardo ^{[3
,4
]}

机构：

[1] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Scotland

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] Univ Bonn, Math Inst, Hausdorff Ctr Math, Bonn, Germany

[4] Univ Edinburgh, Sch Math, Edinburgh, Scotland

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 377卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Stochastic nonlinear wave equation; ergodicity; invariant measure; white noise; GLOBAL WELL-POSEDNESS; NAVIER-STOKES EQUATIONS; CONVERGENCE; RATES; PDES;

D O I：

10.1090/tran/8973

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the 2-dimensional torus. The noise is taken to be slightly more regular than space-time white noise. In this setting, we show existence and uniqueness of an invariant measure for the Markov semigroup generated by the flow over an appropriately chosen Banach space. This extends a result of the second author [Comm. Math. Phys. 377 (2020), pp. 1311-1347] to a situation where the invariant measure is not explicitly known.

引用

页码：345 / 394

页数：50

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