论文标题
三维随机Navier-Stokes方程，马尔可夫开关
Three-Dimensional stochastic Navier-Stokes equations with Markov switching
论文作者
论文摘要
在三维随机纳维尔 - stokes方程的噪声术语中引入了有限状态马尔可夫链，以允许在两种类型的乘法噪声之间过渡。我们将其称为具有马尔可夫开关的随机Navier-Stokes方程。为了解决这样的系统，引入了正规化随机系统的家族。对于每个此类正规化系统，存在独特的强解决方案（从随机分析的意义上），是通过Martingale问题和路径唯一性的方法确定的。通过从正规化解决方案的家族中获得弱收敛序列，并将极限作为三维随机Navier-Stokes方程的解决方案，从而在限制中删除了正则化。
A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier-Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier-Stokes equation with Markov switching.
