The goal of this article is to study the feedback control for non-stationary three-dimensional Navier–Stokes–Voigt equations. Based on the existence, uniqueness, and boundedness result of the weak solutions to the equations, we obtain the existence of solutions to the feedback control system. An existence result for an optimal control problem is also given. We illustrate our main result with an evolutionary hemivariational inequality.

中文翻译：

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非平稳 3D Navier-Stokes-Voigt 方程的反馈控制

本文的目的是研究非平稳三维 Navier-Stokes-Voigt 方程的反馈控制。根据方程弱解的存在性、唯一性和有界性结果，我们得到反馈控制系统解的存在性。还给出了最优控制问题的存在性结果。我们用进化的半变异不等式来说明我们的主要结果。