Unique Ergodicity for a Class of Stochastic Hyperbolic Equations with Additive Space-Time White Noise

被引：3

作者：

Tolomeo, Leonardo ^{[1
]}

机构：

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

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2020年 / 377卷 / 02期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

NAVIER-STOKES EQUATIONS; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; COUPLING APPROACH; GIBBS MEASURE; STATISTICAL-MECHANICS; INVARIANT-MEASURES; WAVE EQUATIONS; DRIVEN; PDES;

D O I：

10.1007/s00220-020-03752-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the d-dimensional torus. This class includes the wave equation for d=1 and the beam equation for d <= 3. We show that the Gibbs measure is the unique invariant measure for this system. Since the flow does not satisfy the strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.

引用

页码：1311 / 1347

页数：37

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