On the Global Existence for a Class of Compressible Non-Newtonian Fluids with Inhomogeneous Boundary Data

Abstract

This paper is concerned to the study of global existence of weak solutions to a class of compressible non-Newtonian fluids in three-dimensional bounded domain. More precisely, we consider an isentropic compressible non-Newtonian fluid with adiabatic constant \(\gamma>\frac{3}{2}\). We study the global existence of an initial boundary value problem with nonhomogeneous Dirichlet boundary conditions by constructing an approximation scheme, energy estimates, and a weak convergence method.