Étude d'un fluide traversant une paroi perforée. I: Comportement limite près de la paroi. (Study of a fluid crossing a perforated sieve. I: Limit behavior near the sieve)
This is part one of a two part paper. The problem investigated is the mathematical one of studying the behaviour of a solution to the steady Stokes equations of hydrodynamics in a region which contains a separating surface with a periodic array of holes (a sieve). It is assumed that the velocity is zero on the sieve and given on the boundary of the region. The mathematical techniques employed are those from homogenization theory and the solution is studied in the limit that the sieve becomes finer. The results proved show that the solution is asymptotically divided into two regions: one in a boundary layer of the sieve, where a periodic structure is developed with high energy dissipation. The second region corresponds to an outer zone. The first part of the paper concentrates on the solution in the boundary layer near the sieve.
scientific article; zbMATH DE number 4008970