On the existence of solution, Lie symmetry analysis and conservation law of magnetohydrodynamic equations

Abstract

The (2+1)-dimensional incompressible and barotropic magnetohydrodynamic flow is studied combined with qualitative and quantitative analysis. The conservation of the energy of this system and the global existence of the solution (U,b) in L2([0,+∞);L2(R2))×L2([0,+∞);L2(R2)) are proved utilizing priori estimate and Galerkin method. We present the general Lie symmetry analysis method to boundary value problem. The Lie symmetry analysis of magnetohydrodynamic equations with infinite boundary is proposed for finding infinitesimal generators, symmetry groups and various analytical solutions. We prove the nonlinear self-adjointness and compute the conservation law for the magnetohydrodynamic equations.