Optimization of a Duality Method for the Compressible Reynolds Equation

Existence result for stationary compressible fluids and asymptotic behavior in thin films

“…We can show that this condition is satisfy in the two-dimensional case taking q large enough and in the 3-dimensional case taking q = 6 (and using the fact that N > 1 3 , M < −1 2 and n < 1). Consequently, the friction term T 2 satisfies…”

“…Within the framework of the compressible fluids, there exist a so called compressible Reynolds equation which is, at least formally, the asymptotic of the Navier-Stokes compressible equations in a thin domain. Contrary to the incompressible classical Reynolds equation, the compressible Reynolds equation is highly nonlinear and has been a subject of many mechanical studies [3,12] or of numerical studies [1,11]. However the literature about the rigorous justification of these equations in the compressible case is not very important.…”