Global behaviour of 1‐D viscous compressible barotropic flows with free boundary and self‐gravitation

Abstract

SUMMARYWe consider an initial-boundary value problem for a system of quasilinear equations for one-dimensional ows of a viscous compressible barotropic uid with large data. An outer pressure (possibly zero) is prescribed on one of the boundaries; also a self-gravitation is taken into account. The case of the stationary pressure with possible degeneration is studied. For a general non-monotone state function, either global estimates for the solution and its stabilization are proved or the growth of the uid volume is bounded from below as t → ∞. For the power state function, in addition, stabilization rate estimates (of the power type) are given. The study is accomplished in the Lagrangian mass co-ordinates.

Recent progress in the mathematical theory of 1D barotropic flow

“…If the outer pressure may also be zero, then the decay rate to the steady state is established in [19].…”

Local strong solution of Navier–Stokes–Poisson equations with degenerated viscosity coefficient

“…There are also very interesting investigations about free boundary value problems for the compressible Navier-Stokes equations with self-gravitation force taken into granted, refer to [14][15][16][17][18][19][20][21][22] and the references therein. Recently, Jang in [16] established the local in time well-posedness of strong solutions to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system in the spherically symmetric and isentropic motion.…”