Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of 2D Density-Dependent Magnetohydrodynamic Equations with Vacuum

Abstract

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to the 2D Cauchy problem on the whole space ${\mathbb{R}}^2$, provided that the initial density and the initial magnetic decay not too slow at infinity. In particular, the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the gradients of velocity, magnetic and pressure.

20 pages. arXiv admin note: substantial text overlap with arXiv:1506.03143, arXiv:1506.02156; text overlap with arXiv:1501.05417, arXiv:1310.1673 by other authors

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Cited by in corpus (3)

• Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows with vacuum
• Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum
• Existence theorems for the Cauchy problem of 2D nonhomogeneous incompressible non-resistive MHD equations with vacuum