On Local Strong Solutions to the Cauchy Problem of Two-Dimensional Density-Dependent Magnetohydrodynamic Equations with Vacuum

Abstract

This paper concerns the Cauchy problem of the 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. We prove that the 2D Cauchy problem of the nonhomogeneous incompressible MHD equations admits a unique local strong solution provided the initial density and the initial magnetic decay not too slow at infinity.

22 pages. arXiv admin note: text overlap with arXiv:1306.4752 by other authors

References in corpus (3)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Global Strong solution with vacuum to the 2D nonhomogeneous incompressible MHD system
• Global existence for the MHD system in critical spaces

Cited by in corpus (6)

• On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum
• Global Strong Solutions to the Compressible Magnetohydrodynamic Equations with Slip Boundary Conditions in 3D Bounded Domains
• Local well-posedness to the 2D Cauchy problem of full compressible magnetohydrodynamic equations with vacuum at infinity
• Supercongruences for Almkvist--Zudilin sequences
• Existence theorems for the Cauchy problem of 2D nonhomogeneous incompressible non-resistive MHD equations with vacuum
• Strong solutions to the Cauchy problem of the two-dimensional non-baratropic non-resistive magnetohydrodynamic equations with zero heat conduction