2015/05/14 by Xia Ye, Jianwen Zhang, Ye, Xia +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1505.03598
openalex publication_date 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The vanishing shear viscosity limit is justified and the convergence rates are obtained. More important, to capture the behavior of the solutions at vanishing shear viscosity, both the boundary-layer thickness and the boundary-layer solution are discussed. As by-products, the global well-posedness of strong solutions with large data is established. The proofs are based on the global (uniform) estimates which are achieved by making a full use of the "effective viscous flux", the material derivatives and the structure of the one-dimensional equations.