Existence And Large-time Behavior Of Global Weak Solutions For A Class Of Compressible Non-Newtonian Fluids

The traditional models describes the fluid motion used mostly in physics and related areas are based on a set of partial differential equations known as the Navier-Stokes equations.These mathematical fluid models are developed on the base of fundamental thermodynamics laws,conservation of mass and mo-mentum of the fluid and conservation of energy.During the last several decades,Navier-Stokes equations are mostly applicable in the field of engineering and in-dustry.In view of its large variety of applications in many natural and industrial systems,this area is of great importance for physicists,applied mathematicians and engineers.Navier-Stokes system is mainly used as central tool for describing fluid dynamics.Research on Navier-Stokes equations and its coupling with other equations have always been the focus of study of nonlinear partial differential equations.We mainly focus on the large-time behaviour and existence of global weak solutions to a class of compressible non-Newtonian fluids.The main results are stated as follows:In three-dimensional-bounded domain,the global existence of weak solution of an initial-boundary value problem for a compressible non-Newtonian fluid is investigated.The solution to the problem is formulated by using the artificial pressure technique,through the approximation scheme and the weak convergence method.The global existence of weak solution for a compressible non-Newtonian fluid with vacuum is established.The large-time behaviour of weak solutions regarding time and data of com-pressible non-Newtonian fluids in R3,under the action of potential force is stud-ied.We describe the large-time behaviour of solutions in a bounded domain,after studying the uniqueness of solutions of the stationary problem as t→∞.Finally,we study the decay estimates of weak solutions of a compressible non-Newtonian fluid with nonlinear constitutive equations in three-dimensional bounded domain.The decay estimates of such solutions are studied with large data.