On steady solutions to vacuumless Newtonian models of compressible flow
Analysis of PDEs
2015-06-16 v3
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 H\"older continuous, which does not generally hold for the classical isentropic model in the presence of vacuum.
Keywords
Cite
@article{arxiv.1306.2580,
title = {On steady solutions to vacuumless Newtonian models of compressible flow},
author = {Michał Łasica},
journal= {arXiv preprint arXiv:1306.2580},
year = {2015}
}
Comments
25 pages. Submitted to a refereed journal in May 2013. Added references and rebuilt introduction, some minor mistakes corrected