含时空局部噪声的二维Navier-斯托克斯方程的大偏差原理
Large deviations principle for 2D Navier-Stokes equations with space time localised noise
摘要：
考虑有界区域上的随机二维Navier-斯托克斯方程。假设随机力在时间上是非退化的和周期性的，它的规律在时间和空间上都有一个局部化的支撑。对Shirikyan [Shi 15]关于指数遍历性的开创性工作中的条件稍加加强，证明了随机系统满足Donsker-Varadhan型大偏差原理.我们的证明是基于[JNPS 15]的一个准则，其中我们需要证明相关的Feynman-Kac半群的一致不可约性和一致Feller性质。
英文摘要：
We consider a stochastic 2D Navier-Stokes equation in a bounded domain. The random force is assumed to be non-degenerate and periodic in time, its law has a support localised with respect to both time and space. Slightly strengthening the conditions in the pioneering work about exponential ergodicity by Shirikyan [Shi15], we prove that the stochastic system satisfies Donsker-Varadhan typle large deviations principle. Our proof is based on a criterion of [JNPS15] in which we need to verify uniform irreducibility and uniform Feller property for the related Feynman-Kac semigroup.
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