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arXiv · 1709.09306

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

Rongchan Zhu·Xiangchan Zhu
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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 $η\in (-\frac{1}{2},0)$.

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Rongchan Zhu, Xiangchan Zhu. 2017-09-29. Strong-Feller property for Navier-Stokes equations driven by space-time white noise. https://arxiv.org/abs/1709.09306

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