Optimal control problems with state constraint governed by Navier-Stokes equations

TL;DR

This paper investigates the existence of optimal solutions and derives the maximum principle for control problems governed by Navier-Stokes equations with state constraints in three dimensions, also providing strong results for two-dimensional cases.

Contribution

It presents new theoretical results on optimal control with state constraints for Navier-Stokes equations, including existence and maximum principle in 3-D and strong results in 2-D.

Findings

Existence of optimal solutions for 3-D Navier-Stokes control problems.

Derivation of maximum principle under state constraints.

Strong results established for 2-D Navier-Stokes control problems.

Abstract

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.