A modified log-Harnack inequality and asymptotically strong Feller property

作者：Xu Lihu^*

来源：Journal of Evolution Equations, 2011, 11(4): 925-942.

DOI：10.1007/s00028-011-0117-z

• Wang type Harnack inequality
• Log-Harnack inequality
• Modified log-Harnack inequality
• Strong Feller property
• Asymptotically strong Feller property
• 2D stochastic Navier-Stokes equation
• Asymptotic coupling

We introduce a new Harnack type inequality, which is a modification of the log-Harnack inequality established by Rockner and Wang and prove that it implies the asymptotically strong Feller property (ASF). This inequality generalizes the criterion for ASF introduced by Hairer and Mattingly. As an example, we show by an asymptotic coupling that the 2D stochastic Navier-Stokes equation driven by highly degenerate but essentially elliptic noise satisfies our modified log-Harnack inequality.

• 出版日期2011-12