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A modified log-Harnack inequality and asymptotically strong Feller property. (English) Zbl 1270.60085
To characterize the asymptotic strong Feller property, a weaker version of the log-Harnack inequality is introduced. In particular, using an asymptotic coupling argument, a weak log-Harnack inequality for the 2D stochastic Navier-Stokes equation driven by highly degenerate but essentially elliptic noise is established, and thus the known asymptotic strong Feller property is re-confirmed.

MSC:
60J60 Diffusion processes
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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