Compressible Navier-Stokes system with general inflow-outflow boundary data

Tongkeun Chang (1) , B J Jin , Antonin Novotny (2)

1 Yonsei University
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

We prove existence of weak solutions to the compressible Navier-Stokes equations in barotropic regime (adiabatic coefficient γ > 3/2, in three dimensions, γ > 1 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 neither on the shape of the inflow/outflow boundaries nor on the shape of the domain. The result applies also to pressure laws that are non monotone on a compact portion of interval [0, ∞).

Keywords: inhomogeneous boundary conditions; Compressible Navier–Stokes system; weak solutions; renormalized continuity equation; large inflow; large outflow *

Domains: Mathematics [math]; Mathematics [math]; Analysis of PDEs [math.AP]

Tongkeun Chang, B J Jin, Antonin Novotny. Compressible Navier-Stokes system with general inflow-outflow boundary data. SIAM Journal on Mathematical Analysis, 2019, 51 (2), pp.1238-1475. ⟨hal-01756728⟩