论文标题
2D Navier-Stokes方程的大偏差原理具有时空局部噪声
Large deviations principle for 2D Navier-Stokes equations with space time localised noise
论文作者
论文摘要
我们考虑一个随机的2D Navier-Stokes方程。假定随机力是非分类的，并且在时间上是周期性的，其定律具有相对于时间和空间的本地化的支持。稍微加强了Shirikyan [Shi15]的开创性工作中的条件，我们证明随机系统满足Donsker-Varadhan典型典型的大偏差原则。我们的证明是基于[JNPS15]的标准，在该标准中，我们需要验证相关的Feynman-kac Semigroup的统一不可约性和统一的伐木属性。
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.
