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arXiv · 1608.07996

Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles

Hui Liu·Hongjun Gao
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Abstract

In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of strong solution are proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as $\beta = 3$. Meanwhile, a small time large deviation principle for the stochastic 3D Navier-Stokes equation with damping is proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as $\beta = 3$.

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Hui Liu, Hongjun Gao. 2016-08-29. Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles. https://arxiv.org/abs/1608.07996

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