带泊松跳的随机Navier-Stokes方程最优控制

摘要

对随机Navier-Stokes方程的讨论,通常的文献都没有考虑Poisson跳对系统的扰动.在假设控制算子为线性时,研究了带Poisson跳的随机Navier-Stokes方程的最优控制问题.利用Burkholder-Davis-Gundy不等式和Gronwall引理证明了最优控制的存在性.%The influence of the Poisson jumps upon the system has not been considered in stochastic Navier-Stokes equation. In this paper,the optimal control in stochastic Navier-Stokes equation with Poisson jumps was discussed on the condition that control operator is linear. Existence of optimal control was proved by application of Burkholder-Davis-Gundy inequality and Gronwall lemma.