5 citations · 14 across the 6 of their papers we have counts for
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A Stochastic Representation for Backward Incompressible Navier-Stokes Equations
Xicheng Zhang
By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar t…
Smooth Solutions of Non-linear Stochastic Partial Differential Equations
Xicheng Zhang
In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to…
Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
Jiagang Ren, Xicheng Zhang
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result c…
Tamed 3D Navier-Stokes Equation: Existence, Uniqueness and Regularity
Michael Röckner, Xicheng Zhang
In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth s…
On Stochastic Evolution Equations with non-Lipschitz Coefficients
Xicheng Zhang
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochasti…