Strong solutions to the Cauchy problem of the two-dimensional non-baratropic non-resistive magnetohydrodynamic equations with zero heat conduction

2018/01/21 by Xin Zhong, Zhong, Xin
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1801.07589

openalex publication_date 2018/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy estimates, we prove that there exists a local strong solution provided the initial density and the initial magnetic decay not too slow at infinity.

Related

• Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivity
• Existence theorems for the Cauchy problem of 2D nonhomogeneous incompressible non-resistive MHD equations with vacuum
• Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data
• Strong Solutions for Three-dimensional Nonhomogeneous Incompressible Heat Conducting Magnetohydrodynamic Equations with Vacuum
• Entropy-bounded solutions to the Cauchy problem of compressible planar non-resistive magnetohydrodynamics equations with far field vacuum