On steady solutions to vacuumless Newtonian models of compressible flow
arXiv:1306.2580 · doi:10.1088/0951-7715/27/11/2663
Abstract
We prove the existence of weak solutions to the steady compressible Navier-Stokes system in the barotropic case for a class of pressure laws singular at vacuum. We consider the problem in a bounded domain in R^2 with slip boundary conditions. Due to appropriate construction of approximate solutions used in proof, obtained density is bounded away from 0 (and infinity). Owing to a classical result by P.-L. Lions, this implies that density and gradient of velocity are at least Hölder continuous, which does not generally hold for the classical isentropic model in the presence of vacuum.
25 pages. Submitted to a refereed journal in May 2013. Added references and rebuilt introduction, some minor mistakes corrected