Strong-Feller property for Navier-Stokes equations driven by space-time white noise

2017/09/27 by Zhu, Rongchan, Zhu, Xiangchan
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1709.09306

Abstract

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∈ (-(1)/(2),0).

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