Global Classical Solutions of Viscous Liquid-gas Two-phase Flow Model

In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence of global classical solutions to the compressible Navier-Stokes equations was obtained by using the continuity methods under the assumption that the initial energy is sufficiently small.Comment: 20 page

Local well-posedness and regular criterion of compressible，viscous，micropolar fluid

可压微极性流体是指流体中散布着粒子的悬浮液，比如血液、有添加剂的润滑油和聚合物溶液等。与经典的可压Navier-Stokes方程主要差别是放弃Euler-Cauchy应力原理的假设，考虑流体运动时存在非零应力偶张量的情况，其结果导致非对称的应力张量。由于流体内部的这些粒子被非对称的张力作用，并且这些粒子本身的相互作用能够影响流体本身，流体呈现出非牛顿流体的特性。这是一类很重要的非牛顿流体，被认为是经典可压Navier-Stokes方程的推广而被人们广泛的关注。 本文考虑在初始密度在某些子区域上含有真空并且初始值满足某种相容性条件的情况下，局部强解的存在性。首先，我们采用线性化方法将微极性流体...A continuous fluid mechanics with randomly oriented particles suspended in the medium is assigned to the rotation or spin of molecular subunits, such as blood, additive lubricant and liquor of polymer etc. Compared with classical compressible Navier-Stokes equation, the main difference is to give up the hypothesis of Euler-Cauchy principle of stress and the movement with non-zero stress of tenser....学位：博士后院系专业：数学科学学院数学与应用数学系_数学学号：201017005