Well-posedness of a quasilinear hyperbolic fluid model

Racke, Reinhard; Saal, Jürgen

Well-posedness of a quasilinear hyperbolic fluid model

Files

hypnsloc.pdf(312.84 KB)

Date

2010

Authors

Racke, Reinhard

Saal, Jürgen

Series

Konstanzer Schriften in Mathematik; 267

Publication type

Working Paper/Technical Report

Abstract

We replace a Fourier type law by a Cattaneo type law in the derivation of the fundamental equations of fluid mechanics. This leads to hyperbolicly perturbed quasilinear Navier-Stokes equations.For this problem the standard approach by means of quasilinear symmetric hyperbolic systems seems to fail by the fact that finite propagation speed might not be expected. Therefore a somewhat different approach via viscosity solutions is developed in order to prove higher regularity energy estimates for the linearized system. Surprisingly, this method yields stronger results than previous methods, by the fact that we can relax the regularity assumptions on the coefficients to a minimum. This leads to a short and elegant proof of a local-in-time existence result for the corresponding first order quasilinear system, hence also for the original hyperbolicly perturbed Navier-Stokes equations.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

RACKE, Reinhard, Jürgen SAAL, 2010. Well-posedness of a quasilinear hyperbolic fluid model

BibTex

@techreport{Racke2010Wellp-699,
  year={2010},
  series={Konstanzer Schriften in Mathematik},
  title={Well-posedness of a quasilinear hyperbolic fluid model},
  number={267},
  author={Racke, Reinhard and Saal, Jürgen}
}

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