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