Global Existence of Strong Solutions to Compressible Navier-Stokes System with Degenerate Heat Conductivity in Unbounded Domains

2018/09/03 by Kexin Li, Li, Kexin, Xuanlin Shu +3 · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1809.00609

Abstract

In one-dimensional unbounded domains, we prove global existence of strong solutions to the compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity κ depends on the temperature θ according to κ=κθ^β(β>0). Note that the conditions imposed on the initial data are the same as those of the constant heat conductivity case ([Kazhikhov, A. V. Siberian Math. J. 23 (1982), 44-49]) and can be arbitrarily large. Therefore, our result generalizes Kazhikhov's result for the constant heat conductivity case to the degenerate and nonlinear one.

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