Incompressible Magnetohydrodynamic Flow with Zero Resistivity

Abstract

We prove the existence of both local and global smooth solutions to the Cauchy problem in ${\mathbb{R}}^3$ for the incompressible magnetohydrodynamics (MHD) system. We also prove that the solution to the incompressible MHD system can be obtained as the incompressible limit of the corresponding compressible system. We apply methods in extracting weak dissipative structure which were suggested by Lei-Liu-Zhou.

This paper has been withdrawn by the author due to a crucial error in the proof

References in corpus (4)

• Global Solutions for Incompressible Viscoelastic Fluids
• On well-posedness of the Cauchy problem for MHD system in Besov spaces
• Incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity
• Global Solutions of the Equations of 3D Compressible Magnetohydrodynamics with Zero Resistivity