Global Existence of 2D Slightly Compressible Viscous Magneto-Fluid Motion

E. Casella, P. Secchi and P. Trebeschi

Abstract: In this paper we study the equations of magneto-hydrodynamics for a 2D compressible viscous fluid, under periodic boundary conditions. It is well known that, as the Mach number goes to zero, the solutions of the compressible model approximate that of the incompressible one. In dimension 2 such incompressible limit solution is global in time. We prove that also the compressible solution exists for all time, provided that the Mach number is sufficiently small and the initial data are almost incompressible.

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