On a relaxation approximation of the 2-D incompressible magnetohydrodynamic equations

Abstract

We study the Cauchy problem of a 2-D hyperbolic relaxation system for the incompressible magnetohydrodynamic (MHD) equations, which is related with the scientific computational aspects. We prove that this relaxed problem possesses a global strong solution, provided that the relaxation parameter is small and the appropriate norm of the initial data is not very large. We also show that such global solution converges to the one of the original incompressible MHD equations, as the relaxation parameter goes to zero.