Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs

被引：0
作者：
E Weinan
Di Liu
机构：
[1] Princeton University,Department of Mathematics and Program in Applied and Computational Mathematics
[2] Princeton University,Program in Applied and Computational Mathematics
[3] Peking University,School of Mathematical Sciences
来源：
Journal of Statistical Physics | 2002年 / 108卷
关键词：
Ergodicity; invariant measures; stationary processes; infinite-dimensional random dynamical systems; stochastic partial differential equations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present a general strategy for proving ergodicity for stochastically forced nonlinear dissipative PDEs. It consists of two main steps. The first step is the reduction to a finite dimensional Gibbsian dynamics of the low modes. The second step is to prove the equivalence between measures induced by different past histories using Girsanov theorem. As applications, we prove ergodicity for Ginzburg–Landau, Kuramoto–Sivashinsky and Cahn–Hilliard equations with stochastic forcing.
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页码：1125 / 1156
页数：31
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