Global Existence Versus Blow-Up for Multidimensional Hyperbolized Compressible Navier–Stokes Equations

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2023
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Hu, Yuxi
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SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics (SIAM). 2023, 55(5), pp. 4788-4815. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/22m1497468
Zusammenfassung

We consider the nonisentropic compressible Navier–Stokes equations in two or three space dimensions for which the heat conduction of Fourier’s law is replaced by Cattaneo’s law and the classical Newtonian flow is replaced by a revised Maxwell flow. We show that a physical entropy exists for this new model. For two special cases, we show the global well-posedness of solutions with small initial data and the blow-up of solutions in finite time for a class of large initial data. Moreover, for vanishing relaxation parameters, the solutions (if they exist) are shown to converge to solutions of the classical system.

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510 Mathematik
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compressible Navier–Stokes equations, Cattaneo’s law, Maxwell flow, global solutions, blow-up, relaxation limit
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ISO 690HU, Yuxi, Reinhard RACKE, 2023. Global Existence Versus Blow-Up for Multidimensional Hyperbolized Compressible Navier–Stokes Equations. In: SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics (SIAM). 2023, 55(5), pp. 4788-4815. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/22m1497468
BibTex
@article{Hu2023-09-26Globa-68995,
  year={2023},
  doi={10.1137/22m1497468},
  title={Global Existence Versus Blow-Up for Multidimensional Hyperbolized Compressible Navier–Stokes Equations},
  number={5},
  volume={55},
  issn={0036-1410},
  journal={SIAM Journal on Mathematical Analysis},
  pages={4788--4815},
  author={Hu, Yuxi and Racke, Reinhard}
}
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