Compressible fluids and active potentials

Peter Constantin, Theodore D. Drivas, Huy Q. Nguyen, Federico Pasqualotto

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential.

Original languageEnglish (US)
Pages (from-to)145-180
Number of pages36
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number1
DOIs
StatePublished - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Keywords

  • Compressible flow
  • Global existence
  • Shallow water
  • Slender jet

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