Time Periodic Solutions For A Three-Dimensional Non-conservative Compressible Two-fluid Model

In this paper,we consider a non-conservative compressible two-fluid model with constant viscosity coefficients and unequal pressure functions P+?P-in periodic domains of R3.The main result of this paper is the existence of time periodic solu-tions of this model.To begin with,we introduce a completely continuous operator related to the solutions of the model.Then,we deduce some delicate a priori estimates based on the standard energy method.Finially,we prove the existence of time periodic solutions by the topological degree theory under some smallness assumptions.In Chapter 1,we give the backgrounds of the non-conservative compressible two-fluid model and list the progress of the well-posedness theory of this model and some useful lemmas.In Chapter 2,we introduce the operator used in the topological degree theory.Then,we deduce some basic energy estimates.Finally,we consider the existence of time periodic solutions of the non-conservative compressible two-fluid model in periodic domains of R3.In Chapter 3,we give some remarks of this paper.