Global Solutions for the Rotating Magnetohydrodynamics System in the Scaling Critical Sobolev Space

Abstract

We consider the initial value problem for the incompressible magnetohydrodynamics system with the Coriolis force in the whole space R³. We prove the global in time existence and the uniqueness of solutions for large initial data in the scaling critical Sobolev space when the speed of rotation is sufficiently high. In order to control the large magnetic fields, we introduce a modified linear solution for the velocity, and show its smallness in a suitable space-time norm by means of the dispersive effect of the Coriolis force.