Mixtures of nonhomogeneous viscoelastic incompressible fluids governed by the Kelvin-Voigt equations

Abstract

An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is established: velocity, density and pressure. Under additional regularity assumptions, we also prove the uniqueness of the solution.