Asymptotic analysis of a viscous fluid layer separated by a thin stiff stratified elastic plate
Julia Orlik, Grigory P. Panasenko, Ruxandra Stavre · Applicable Analysis · 2019
A three-dimensional model for a viscous fluid layer separated in two parts by a thin stratified stiff plate is considered. This problem depends on a small parameter ϵ, which is the ratio of the thickness of the plate and that of each of the two parts of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate's Young modulus is of order ε−3, i.e. it is great, while its density is of order 1. At the solid–fluid interfaces, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is established for the partial sums of the asymptotic expansion. The limit problem contains a non-standard interface condition for the Stokes equations. The existence, uniqueness and regularity of its solution are proved.