On the time-dependent grade-two model for the magnetohydrodynamic flow: 2D case

TL;DR

This paper proves the existence and uniqueness of solutions for a time-dependent magnetohydrodynamic flow model of a second grade fluid in 2D, providing a foundation for numerical analysis of such flows.

Contribution

It establishes the mathematical well-posedness of a 2D time-dependent MHD second grade fluid model, enabling future numerical simulations.

Findings

Existence of a weak solution is proven.

Uniqueness of the solution is demonstrated.

Methodology can be adapted for finite-element numerical schemes.

Abstract

In this paper we discuss the MHD flow of a second grade fluid, in particular we prove the existence and uniqueness of a weak solution of a time-dependent grade two fluid model in a two-dimensional Lipschitz domain. We follow the methodology of Girault and Saadouni (Ref.[3]), i.e , we use a constructive method which can be adapted to the numerical analysis of finite-element schemes for solving this problem numerically.