Reynolds type equation for a thin flow under intensive transverse percolation
С. А. Назаров, Juha Videman · Mathematische Nachrichten · 2004
Abstract A two‐dimensional Reynolds type equation is derived and justified for a three‐dimensional viscous incompressible flow, taking place between two smooth fixed adjacent curved walls, under intensive percolation. Resulting from the dimension reduction, the model is proved to admit fluxes of order 1 = h0 with respect to the relative thickness h, a small parameter. Thus, velocities are allowed to be of order h−1, which is just the case where linear and nonlinear terms have the same asymptotic powers O(h−3). Boundary layers are also taken into account and estimates obtained for the remainder terms in the asymptotic representation formulae. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)