Asymptotic log-Harnack inequality for the 2D Ericksen-Leslie model system with degenerate noise and damping. (English) Zbl 1540.35479
Summary: In this paper, we consider a 2D liquid crystal model with damping and examine some asymptotic behaviors of the strong solution. More precisely, we establish the asymptotic log-Harnack inequality for the transition semigroup associated with a simplified liquid crystal model driven by an additive degenerate noise via the asymptotic coupling method. As consequences of the asymptotic log-Harnack inequality, we derive the gradient estimate, the asymptotic irreducibility, the asymptotic strong Feller property, the asymptotic heat kernel estimate and the ergodicity.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
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