Blow-up for hyperbolized compressible Navier-Stokes equations

Reinhard Racke; Reinhard Racke

doi:10.3934/cam.2025022

Communications in Analysis and Mechanics

2025, Volume 17, Issue 2: 550-581. doi: 10.3934/cam.2025022

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Blow-up for hyperbolized compressible Navier-Stokes equations

Reinhard Racke ^,

Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany

Received: 13 November 2024 Revised: 08 May 2025 Accepted: 14 May 2025 Published: 21 May 2025
35L60, 35B44

This work reports on initial value problems to hyperbolized compressible Navier-Stokes equations. Local existence and global existence for small data are addressed as well as singular limits for vanishing relaxation parameters. Then blow-up results for one- and multi-dimensional models are presented using ideas from T.C. Sideris from the 1980s.
- compressible Navier-Stokes equations,
- relaxation,
- hyperbolic systems,
- singular limits,
- blow-up
Citation: Reinhard Racke. Blow-up for hyperbolized compressible Navier-Stokes equations[J]. Communications in Analysis and Mechanics, 2025, 17(2): 550-581. doi: 10.3934/cam.2025022

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Abstract

This work reports on initial value problems to hyperbolized compressible Navier-Stokes equations. Local existence and global existence for small data are addressed as well as singular limits for vanishing relaxation parameters. Then blow-up results for one- and multi-dimensional models are presented using ideas from T.C. Sideris from the 1980s.

References

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