时空白噪声驱动下Navier-斯托克斯方程的强Feller性质
Strong-Feller property for Navier-Stokes equations driven by space-time white noise
摘要：
本文利用MartinHairer在[Hai 14]中引入的正则结构理论，证明了时空白噪声驱动的二维或三维Navier-Stokes（N-S）方程的马尔可夫半群的强Feller性质.这意味着时空白噪声驱动的二维N-S方程从$η\in (-\frac{1}{2},0)$的$C^η$中的每一个初始点开始的全局适定性。
英文摘要：
In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in [Hai14]. This implies global well-posedness of 2D N-S equation driven by space-time white noise starting from every initial point in $C^η$ for $η\in (-\frac{1}{2},0)$.
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