Global existence versus blow-up for multi-d hyperbolized compressible Navier-Stokes equations

Hu, Yuxi; Racke, Reinhard

Global existence versus blow-up for multi-d hyperbolized compressible Navier-Stokes equations

Files

Hu_2-10ag10bz2dxdl8.pdf(485.68 KB)

Date

2022

Authors

Hu, Yuxi

Racke, Reinhard

Series

Konstanzer Schriften in Mathematik; 405

Publication type

Working Paper/Technical Report

Publication status

Submitted

Abstract

We consider the non-isentropic 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 it exists) are shown to converge to solutions of the classical system.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

HU, Yuxi, Reinhard RACKE, 2022. Global existence versus blow-up for multi-d hyperbolized compressible Navier-Stokes equations

BibTex

@techreport{Hu2022-04-27T17:25:04ZGloba-57380,
  year={2022},
  series={Konstanzer Schriften in Mathematik},
  title={Global existence versus blow-up for multi-d hyperbolized compressible Navier-Stokes equations},
  number={405},
  author={Hu, Yuxi and Racke, Reinhard}
}

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