Global small solution to the 2D MHD system with a velocity damping term

TL;DR

This paper proves the global existence, uniqueness, and decay rates of smooth solutions for the 2D incompressible MHD system with velocity damping, when initial data is near equilibrium.

Contribution

It establishes the first global well-posedness results and explicit decay rates for the 2D MHD system with damping, under near-equilibrium initial conditions.

Findings

Global existence and uniqueness of smooth solutions

Explicit decay rates for Sobolev norms

Results hold for initial data close to equilibrium

Abstract

This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also given.