Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity

2014/05/01 by Xianpeng Hu, Fanghua Lin, Hu, Xianpeng +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1405.0082

openalex publication_date 2014/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated parabolic-hyperbolic system. The solution is constructed as a small perturbation of a constant background in critical spaces. The deformation gradient has been introduced to decouple the subtle coupling between the flow and the magnetic field. The L¹ dissipation of the velocity is obtained.

Citations

• Global small solutions to three-dimensional incompressible MHD system
• Some mathematical questions related to the mhd equations

Cited by

• Global Well-posedness of the Incompressible Magnetohydrodynamics

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