Almost periodic homogenization of a generalized Ladyzhenskaya model for incompressible viscous flow

TL;DR

This paper proves the existence and homogenization of a generalized Ladyzhenskaya model for incompressible viscous flow with non-constant density, using sigma-convergence and compactness methods.

Contribution

It introduces an existence result for non-stationary Ladyzhenskaya equations with variable density and applies a novel homogenization approach combining sigma-convergence and compactness.

Findings

Established existence of solutions for non-stationary Ladyzhenskaya equations

Developed a homogenization framework for variable density fluid models

Applied sigma-convergence to nonlinear Navier-Stokes type equations

Abstract

The paper deals with the existence and almost periodic homogenization of some model of generalized Navier-Stokes equations. We first establish an existence result for non-stationary Ladyzhenskaya equations with a given non constant density. The external force depends nonlinearly on the velocity. Next, to proceed with homogenization, as the density of the fluid is non constant, we combine the sigma-convergence method with some compactness arguments.