×

Global existence of 2D slightly compressible viscous magneto-fluid motion. (English) Zbl 1001.76117

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

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
PDFBibTeX XMLCite
Full Text: EuDML