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

TL;DR

This paper investigates a mathematical model for a mixture of nonhomogeneous, incompressible viscoelastic fluids governed by Kelvin-Voigt equations, establishing existence and uniqueness of solutions under certain conditions.

Contribution

It provides the first proof of global-in-time weak solutions for the Kelvin-Voigt system with non-constant density and viscosity.

Findings

Existence of global weak solutions for the system.

Uniqueness of solutions under additional regularity.

Mathematical framework for nonhomogeneous viscoelastic fluid mixtures.

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.