Optimal control for 3D stochastic Navier-Stokes equations

摘要

Loeb space methods are used to prove existence of an optimal control for general 3D stochastic Navier-Stokes equations with multiplicative noise. The possible non-uniqueness of the solutions mean that it is necessary to utilize the notion of a non-standard approximate solution developed in the paper by N. J. Cutland and Keisler H. J. 2004, Global attractors for 3-dimensional stochastic Navier-Stokes equations, Journal of Dynamics and Differential Equations, pp. 16205-16266, for the study of attractors.