Large-time Behavior of Magnetohydrodynamics with Temperature-Dependent Heat-Conductivity

2019/10/12 by Bin Huang, Huang, Bin, Xiaoding Shi +3 · 1 citation
Engineering · Mathematics · #35Q35 #76N10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1910.05579

openalex publication_date 2019/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the large-time behavior of strong solutions to the equations of a planar magnetohydrodynamic compressible flow with the heat conductivity proportional to a nonnegative power of the temperature. Both the specific volume and the temperature are proved to be bounded from below and above independently of time. Moreover, it is shown that the global strong solution is nonlinearly exponentially stable as time tends to infinity. Our result can be regarded as a natural generalization of the previous ones for the compressible Navier-Stokes system to MHD system with either constant heat-conductivity or nonlinear and temperature-dependent heat-conductivity.

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• Global well-posedness of planar MHD system without heat conductivity

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