Weak solutions to the time-fractional g-Navier-Stokes equations and optimal control

TL;DR

This paper investigates the existence and uniqueness of weak solutions to time-fractional g-Navier-Stokes equations in 2D and addresses an optimal control problem related to these equations.

Contribution

It introduces the time-fractional g-Navier-Stokes equations and establishes the existence, uniqueness, and optimal control solutions for these equations.

Findings

Proved existence and uniqueness of weak solutions

Developed Galerkin approximation method for solutions

Solved an optimal control problem for the equations

Abstract

In this paper we introduce the $g-$Navier-Stokes equations with time-fractional derivative of order $\alpha\in(0,1)$ in domains of $\mathbb R^2$. We then study the existence and uniqueness of weak solutions by means of Galerkin approximation. Finally, an optimal control problem is considered and solved.