機率研討會
主講者: | 董昭 教授 (中國科學院) |
講題: | Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise |
時間: | 2013-11-18 (Mon.) 15:30 - 17:00 |
地點: | 數學所 617 研討室 (台大院區) |
Abstract: | Consider the two-dimensional, incompressible Navier-Stokes equations on the torus $T^{2}$ = $[-\pi, \pi]^2$ driven by a degenerate noise $dw_t$=v$\Delta$$w_t$dt+B($Kw_t$,$w_t$)dt+$\sum_{i=1}^{m}$$q_i$($W_t$)$e_i$d$B_i$(t)...(0.1) We prove that the semigroup $P_t$ generated by the solutions to (0.1) has asymptotically strong Feller property. Moreover, we also prove that semigroup ${P_t}_(t\geq0)$ is exponentially ergodic in some sense. |
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