具退化热传导系数的一维可压缩黏性反应气体方程组的柯西问题

Global Strong Solutions to the Cauchy Problem of One Dimensional Compressible Viscous Reactive Gas with Degenerate Heat Conductivity

摘要: 研究了一维全空间上可压缩黏性反应气体方程组的柯西问题，对于热传导系数为温度的幂函数情形，证明了大初值强解的整体存在性。特别地，热传导系数为温度的幂函数导致方程发生退化，这使得密度和温度的正的上下界估计更加困难。

Abstract: This paper considers the Cauchy problem of the one dimensional compressible viscous reactive gas. For the case that the heat conductivity is proportional to a positive power of the temperature, the global existence of strong solutions with large initial data is established. In particular, it’s more difficult to derive the lower and upper bounds of both the density and temperature due to the degenerate heat conductivity.