Global well-posedness of the MHD equations in a homogeneous magnetic field

Abstract

In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the initial velocity is close to 0 and the initial magnetic field is close to a homogeneous magnetic field in the weighted Hölder space, where the closeness is independent of the dissipation coefficients.

41 pages

Cited by in corpus (3)

• Global classical solutions of 3D viscous MHD system without magnetic diffusion on periodic boxes
• Large time behavior of solutions to 3-D MHD system with initial data near equilibrium
• Long time behavior of Alfvén waves in a flowing plasma: mathematical analysis on the generation of the magnetic island