2014/05/01 by Xianpeng Hu, Hu, Xianpeng
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1405.0274
openalex publication_date 2014/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The existence of global-in-time classical solutions to the Cauchy problem of compressible magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linear structure is a degenerated hyperbolic-parabolic system. The solution is constructed as a small perturbation of a constant background in critical spaces. The deformation gradient is introduced to decouple the subtle coupling between the flow and the magnetic field. The L1 dissipation for the velocity is obtained, and the L2 dissipations for the density and the magnetic field are also achieved.