Strong solutions to the 2D Cauchy problem of nonhomogeneous magnetohydrodynamic equations with vacuum

Journal of Mathematical Physics, Volume 61, Issue 10, October 2020. In this paper, we study the strong solutions to the Cauchy problem of nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact support. If both the initial density and the initial magnetic field decay not too slow at infinity, the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution.