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arXiv · 1705.07022

A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

I. S. Ciuperca·E. Feireisl·M. Jai·A. Petrov
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Abstract

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the 1D case.

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I. S. Ciuperca, E. Feireisl, M. Jai, A. Petrov. 2017-05-19. A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations. https://arxiv.org/abs/1705.07022

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