The inviscid and non-resistive limit in the cauchy problem for 3-D nonhomogeneous incompressible magneto-hydrodynamics

In this paper, the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics (MHD) in ℝ3. We prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system. The convergence rate is also obtained simultaneously.