Hyperbolic compressible Navier-Stokes equations

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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.

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ISO 690HU, Yuxi, Reinhard RACKE, 2020. Hyperbolic compressible Navier-Stokes equations. In: Journal of Differential Equations. Elsevier. 2020, 269(4), pp. 3196-3220. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2020.02.025
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@article{Hu2020Hyper-47267.2,
  year={2020},
  doi={10.1016/j.jde.2020.02.025},
  title={Hyperbolic compressible Navier-Stokes equations},
  number={4},
  volume={269},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={3196--3220},
  author={Hu, Yuxi and Racke, Reinhard}
}
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