A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations
研究了受乘性高斯噪声扰动的二维纳维-斯托克斯方程的速度跟踪问题，控制通过带有不确定性的边界注入/抽吸装置实现，证明了状态方程解的存在唯一性和最优解的存在性。
Abstract We study a stochastic velocity tracking problem for the 2D-Navier–Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty, modeled by stochastic non-homogeneous Navier-slip boundary conditions. We show the existence and uniqueness of the solution to the state equation, and prove the existence of an optimal solution to the control problem.