论文标题
随机2-D NAVIER-Stokes方程的动态编程由Levy Noise强制
Dynamic Programming of Stochastic 2-D Navier-Stokes Equations Forced by Levy Noise
论文作者
论文摘要
在本文中，我们研究了随机2D Navier-Stokes方程的最佳反馈控制综合，驱动征费型噪声具有作用在状态方程上的分布式随机控制过程。我们使用动态编程方法来解决此控制问题，该方法涉及研究二阶无限尺寸汉密尔顿 - 雅各布 - 贝尔曼（HJB）方程，该方程包括由与随机控制问题相关的征费量的全差异操作员组成的。使用与随机2D Navier-Stokes方程相对应的过渡半群的正规化属性，我们在加权功能空间中为HJB方程获得了平滑的解决方案，并解决了所得的反馈控制问题。
In this article, we study optimal feedback control synthesis of stochastic 2D Navier-Stokes equations perturbed Levy type noise with distributed stochastic control process acting on the state equation. We use the dynamic programming approach to solve this control problem which involves the study of second order infinite dimensional Hamilton- Jacobi-Bellman (HJB) equation consisting of an integro-differential operator with Levy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic 2D Navier-Stokes equation, we obtain a smooth solution in weighted function space for the HJB equation and solve the resultant feedback control problem.
