Continuity equation and vacuum regions in compressible flows
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🧮 math.AP
keywords
continuitysolutionscompressibleequationequationsregionsvacuumweak
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We investigate the creation and properties of eventual vacuum regions in the weak solutions of the continuity equation, in general, and in the weak solutions of compressible Navier--Stokes equations, in particular. The main results are based on the analysis of renormalized solutions to the continuity and pure transport equations and their inter-relations which are of independent interest.
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