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

0489055 - MÚ 2019 RIV SG eng J - Journal Article
Ciuperca, I. S. - Feireisl, Eduard - Jai, M. - Petrov, A.
A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations.
Mathematical Models and Methods in Applied Sciences. Roč. 28, č. 4 (2018), s. 697-732. ISSN 0218-2025. E-ISSN 1793-6314
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : compressible fluids * stationary Navier-Stokes equations * thin films
OECD category: Pure mathematics
Impact factor: 3.127, year: 2018
https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185

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 one-dimensional case.
Permanent Link: http://hdl.handle.net/11104/0283541