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

2017/05/19 by I. S. Ciuperca, Ionel Sorin Ciuperca, Eduard Feireisl +9
Engineering · Mathematics · #35Q30 #76A20 #76D05 #76D08 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #math.AP #msc:35Q30 #msc:76A20 #msc:76D05 #msc:76D08 #msc:76N10

paper · pdf · doi:10.48550/arxiv.1705.07022

arxiv created 2017/05/19 · openalex publication_date 2017/05/19 · arxiv updated 2017/05/22 · openalex created_date 2019/07/30 · openalex updated_date 2026/08/01

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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