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WELL-POSEDNESS OF REYNOLDS AVERAGED EQUATIONS FOR COMPRESSIBLE FLUIDS WITH A VANISHING PRESSURE
  • ÉMILE DELÉAGE
ÉMILE DELÉAGE
Aix-Marseille Universite

Corresponding Author:emile.deleage@univ-amu.fr

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Abstract

We show that the Reynolds averaged equations for compressible fluids (neglecting third order correlations) are well-posed in H s when the pressure vanishes in dimensions d=2 and 3. In order to do this, we show that the system is Friedrichs-symmetrizable. This model belongs to the class of non-conservative hyperbolic systems. Hence the usual symmetrisation method for conservation laws can not be used here.
16 May 2023Submitted to Mathematical Methods in the Applied Sciences
16 May 2023Submission Checks Completed
16 May 2023Assigned to Editor
24 May 2023Review(s) Completed, Editorial Evaluation Pending
10 Jun 2023Reviewer(s) Assigned
23 Aug 2023Editorial Decision: Revise Major
06 Sep 20231st Revision Received
09 Sep 2023Submission Checks Completed
09 Sep 2023Assigned to Editor
09 Sep 2023Review(s) Completed, Editorial Evaluation Pending
10 Sep 2023Reviewer(s) Assigned
12 Sep 2023Editorial Decision: Accept