Incompressible Magnetohydrodynamic Flow with Zero Resistivity

TL;DR

This paper establishes the existence of smooth solutions for the incompressible MHD equations in three dimensions and shows they can be derived as limits of compressible systems, advancing theoretical understanding of MHD flows.

Contribution

It proves both local and global existence of smooth solutions and connects incompressible and compressible MHD systems through a limiting process.

Findings

Existence of local and global smooth solutions for 3D incompressible MHD.

Incompressible solutions can be obtained as limits of compressible MHD systems.

Application of weak dissipative structure methods in MHD analysis.

Abstract

We prove the existence of both local and global smooth solutions to the Cauchy problem in $\R^3$ 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.