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arXiv · 1306.2580

On steady solutions to vacuumless Newtonian models of compressible flow

Michał Łasica
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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.

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Michał Łasica. 2013-10-18. On steady solutions to vacuumless Newtonian models of compressible flow. https://doi.org/10.1088/0951-7715%2F27%2F11%2F2663

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