Approximation of a Class of Incompressible Third Grade Fluids Equations

Abstract

This paper discusses the approximation of weak solutions for a class of incompressible third grade fluids equations. We first introduce a family of perturbed slightly compressible third grade fluids equations (depending on a positive parameterϵ) which approximate the incompressible equations asϵ→0+. Then we prove the existence and uniqueness of weak solutions for the slightly compressible equations and establish that the solutions of the slightly compressible equations converge to the solutions of the incompressible equations.