数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1077-1086.

• 论文 • 上一篇    

多介质流体动力学系统的弱解

刘树君   

  1. 南京财经大学应用数学学院 南京 210023
  • 收稿日期:2018-07-06 修回日期:2018-12-28 发布日期:2019-11-08
  • 作者简介:刘树君,E-mail:shujunliu@nuaa.edu.cn
  • 基金资助:
    国家自然科学基金(11872201,11572148)

Weak Solutions for the Systems of Multifluid Flows

Liu Shujun   

  1. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023
  • Received:2018-07-06 Revised:2018-12-28 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11872201, 11572148)

摘要: 该文研究了多介质流体动力学系统的弱解.包括欧拉坐标下的等熵气体动力学系统和一个河流方程组.相比单介质系统,多介质系统会产生额外的线性退化场,且其对应的粘性系统右边的人工粘性项会在线性退化方向产生奇性.利用线性退化方向的一致BV估计,结合补偿列紧方法和粘性消失法得到了上述系统大初值问题弱解的全局存在性.

关键词: 多介质流体力学, 补偿列紧方法, 粘性消失法

Abstract: In this paper, we study the weak solutions for the systems of multifluid flows, which includes the system of isentropic gas dynamics in Eulerian coordinates and a system arising from river flows. There are more linearly degenerate fields compared with single-component system, and singularities in these linearly degenerate fields emerge when considering the corresponding vanishing viscosity system. we obtain the existence of global solutions for the system of multifluid flows by analyzing the uniform BV estimates in linearly degenerate fields, coupled with the compensated compactness method and the vanishing viscosity method.

Key words: Multifluid flow, Compensated compactness, Vanishing viscosity method

中图分类号: 

  • O175.2