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 parameter ) which approximate the incompressible equations as → 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.] ≥ 0, 1 > 0, ≥ 0,Also, Busuioc and Iftimie in [5] proved that the third grade fluids equations (3) possess a global solution if the initial value Hindawi Publishing Corporation