TY - JOUR
T1 - Gibbsian dynamics and invariant measures for stochastic dissipative PDEs
AU - Weinan, E.
AU - Liu, Di
N1 - Funding Information:
We are very grateful to J. Mattingly and Ya. Sinai for many stimulating discussions concerning the topics here. Weinan E’s work is partially supported by NSF via a PFF award.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
KW - Ergodicity
KW - Infinite-dimensional random dynamical systems
KW - Invariant measures
KW - Stationary processes
KW - Stochastic partial differential equations
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U2 - 10.1023/A:1019747716056
DO - 10.1023/A:1019747716056
M3 - Article
AN - SCOPUS:0141739287
SN - 0022-4715
VL - 108
SP - 1125
EP - 1156
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -