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math.PR2022★ 2 cited
Sharp non-uniqueness of solutions to stochastic Navier-Stokes equations
Weiquan Chen, Zhao Dong, Xiangchan Zhu
In this paper we establish a sharp non-uniqueness result for stochastic -dimensional () incompressible Navier-Stokes equations. First, for every divergence free initial…
math.PR2014★ 16 cited
Approximating three-dimensional Navier-Stokes equations driven by space-time white noise
Rongchan Zhu, Xiangchan Zhu
In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for t…
math.PR2014
Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions
Michael Rockner, Rongchan Zhu, Xiangchan Zhu
In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be app…