一类粘性依赖于密度的两相流模型的定性研究

两相流是至少一种相为流体的两种物质所组成的系统。在自然界、生物工程、工业生产中广泛存在。近年来，Carrillo等人建立了一个刻画粒子在流体中扩散运动的微观宏观模型。该模型受到了数学、物理等领域专家学者的广泛关注。此后，学者们陆续提出了一系列新的模型来更好描述不同的两相流运动。. 本项目拟研究粘性依赖于密度的两相流模型。该模型中压力是两种密度的函数，而粘性系数只依赖于其中一种密度。压力函数与粘性系数之间的不对等关系为数学研究带来了困难。目前关于这类模型的研究成果还不多见。本项目拟研究如下两个方面的内容：.（1）一维空间中整体经典解的存在性；.（2）二维周期区域中整体强解的存在性和大时间行为。

Two phase flow is a system composed of two substances with at least one phase as fluid. It exists widely in nature, bioengineering and industrial production. In recent years, Carrillo et al. established a microscopic/macroscopic model describing the evolution of particles dispersed in a fluid. The model has been widely concerned by experts and scholars in mathematics, physics and other fields. Since then, a series of new ideas and models have been proposed to describe different two-phase flows.. This project intends to study a two-phase flow model with density-dependent viscosity. The pressure here depends on two variables but the viscosity only depends on one of the densities. The unequal relationship between the pressure function and viscosity coefficient brings difficulties to mathematical research. At present, there are little results on this kind of model. This projectIt is proposed to study the following two problems:.(1)The global existence of classical solution in one dimensional space;.(2)The global existence and large time behavior of strong solution in a two dimensional torus.