Asymptotic Analysis of MHD Systems

TL;DR

This paper investigates the long-term behavior of solutions to Magneto-Hydro-Dynamic systems, employing different mathematical techniques depending on the domain, to establish convergence results.

Contribution

It provides a rigorous asymptotic analysis of MHD systems on both torus and Euclidean space, extending existing methods with new estimates.

Findings

Convergence of strong solutions on ${ m T}^3$ using Schochet's methods.

Application of Strichartz estimates for solutions on ${f m R}^3$.

Development of product laws for mixed-dimensional analysis.

Abstract

In this paper, we study the convergence of strong solutions of a Magneto-Hydro-Dynamic system. On the torus ${\mathbb{T}}^3$, the proof is based on Schochet's methods, whereas in the case of the whole space ${\bf \mathbb{R}^3}$, we use Strichartz's type estimates and a product law's $2D\times3D$.