Global strong solutions to the radially symmetric compressible MHD equations in 2D solid balls with arbitrary large initial data

2023/10/16 by Huang, Xiangdi, Yan, Wei
#35Q30 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.10891

Abstract

In this paper, we prove the global existence of strong solutions to the two-dimensional compressible MHD equations with density dependent viscosity coefficients (known as Kazhikhov-Vaigant model) on 2D solid balls with arbitrary large initial smooth data where shear viscosity μ being constant and the bulk viscosity λ be a polynomial of density up to power β. The global existence of the radially symmetric strong solutions was established under Dirichlet boundary conditions for β>1. Moreover, as long as β∈ (max\1,(γ+2)/(4)\,γ], the density is shown to be uniformly bounded with respect to time. This generalizes the previous result of \cite2022Li,2016Huang,2022Huang of the compressible Navier-Stokes equations on 2D bounded domains where they require β>4/3 and also improves the result of \citechen2022,2015Mei-1,2015Mei-2 of compressible MHD equations on 2D solid balls.

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