Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 59, No. 1, pp. 67-89 (2002)

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

E. Casella, P. Secchi and P. Trebeschi

Dip. di Matematica, Università di Brescia,
Facoltà di Ingegneria, Via Valotti 9, 25133 Brescia -- ITALY

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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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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