Problem on small motions of multicomponent viscous incompressible fluid

Abstract

In this work we study the problem on small motions and normal oscillations of a homogeneous mixture of several viscous incompressible fluids. The considered model is a generalization of the well–known Navier — Stokes equations for the dynamics of a one–component incompressible viscous medium, and it involves the incompressibility and momentum equations. We prove that the corresponding initial boundary value problem is well–posed and solvable. In terms of the Stokes operator, we construct the spectrum and system of eigenelements for the problem on normal oscillations.