The Investigation Of The Stability Of The Boundary Layer To An Inflow Problem For A Class Of Non-Newtonian Fluids

In this thesis,we mainly study the stability of the boundary layer of the inflow problem for one-dimensional isentropic compressible non-Newtonian fluids.Firstly,we obtain the existence and uniqueness of the non-Newtonian boundary layer solution and its attenuation estimation.We also find a special property different from the Newtonian boundary layer,that is,the maximal interval of existence.Finally,we mainly prove that under the small condition,the global solution of the non-Newtonian inflow problem tends toward the corresponding boundary layer solution.The thesis is organized as follows.In Section 1,we describe the purpose and significance of studying the nonNewtonian fluids,as well as the current research status of inflow problems at home and abroad.In Section 2,we illustrate the related definitions and symbols used in this thesis,introduce the inequalities and related lemmas needed in the proof of our main theorem.In Section 3,we firstly study the existence of the boundary layer solution for the non-Newtonian fluids and state our main theorem.Then reformulate the original problem to obtain a initial-boundary value problem,and establish the a priori estimates for proving the main theorems.