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