Asymptotic integration of linear system with high-frequency coefficients and Stokes operator in the main part

Abstract

A linear system of integro-differential equations with Stokes operator in the main part and with rapidly oscillating by time terms is considered. The corresponding stationary limiting (averaged) problem has zero eigenvalue, and corresponding eigenfunction has generalized associated first order function in the Vishik–Lyusternik sense. A complete asymptotic expansion of time-periodic solution is constructed and proved.