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Compressible Navier--Stokes System with General Inflow-Outflow Boundary Data
Chang, T.,Jin, B.J.,Novotný,, A. Society for Industrial and Applied Mathematics 2019 SIAM journal on mathematical analysis Vol.51 No.2
<P>We prove existence of weak solutions to the compressible Navier--Stokes equations in a barotropic regime (adiabatic coefficient <TEX>$\gamma>3/2$</TEX> in three dimensions, <TEX>$\gamma>1$</TEX> in two dimensions) with large velocity prescribed at the boundary and large density prescribed at the inflow boundary of a bounded sufficiently smooth domain, without any restriction on either the shape of the inflow/outflow boundaries or the shape of the domain. The result applies also to pressure laws that are nonmonotone on a compact portion of the interval <TEX>$[0,\infty)$</TEX>.</P>