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Hyperbolic compressible Navier-Stokes equations
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.jde.2020.02.025
Yuxi Hu , Reinhard Racke

Abstract We consider the non-isentropic compressible Navier-Stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by Maxwell's law. These two relaxations, turning the whole system into a hyperbolic one, are not only treated simultaneously, but are also considered in a version having Galilean invariance. For this more complicated relaxed system, the global well-posedness is proved for small data. Moreover, for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system.

中文翻译:

双曲可压缩纳维-斯托克斯方程

摘要 我们考虑了具有双曲热传导的非等熵可压缩纳维-斯托克斯方程和由麦克斯韦定律相应修改的应力张量定律。这两个松弛,将整个系统变成双曲线系统,不仅被同时处理,而且在具有伽利略不变性的版本中也被考虑。对于这个更复杂的松弛系统,证明了小数据的全局适定性。此外,对于消失的松弛参数,解会收敛到经典系统的解。
更新日期:2020-08-01
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