WELL-POSEDNESS OF REYNOLDS AVERAGED EQUATIONS FOR COMPRESSIBLE FLUIDS WITH A VANISHING PRESSURE

Emile Deleage (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 UGA - Université Grenoble Alpes

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.

Mots clés: Hyperbolic systems of partial differential equations; Reynolds averaged equations; Symmetrization; Turbulence

Domaines: Mathématiques [math]

Emile Deleage. WELL-POSEDNESS OF REYNOLDS AVERAGED EQUATIONS FOR COMPRESSIBLE FLUIDS WITH A VANISHING PRESSURE. 2023. ⟨hal-04109590⟩