Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

doi:10.1007/s42967-022-00194-1

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (3): 987-1014.doi: 10.1007/s42967-022-00194-1

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Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

Fangfang Hao¹, Hai-Liang Li^1,2, Luyao Shang¹, Shuang Zhao^1,2

1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;
2. Academy for Multidisciplinary Studies, Capital Normal University, Beijing, 100048, China

收稿日期:2021-12-16 修回日期:2022-03-21 出版日期:2023-09-20 发布日期:2023-08-29
通讯作者: Shuang Zhao,E-mail:shuangzhaomath@163.com E-mail:shuangzhaomath@163.com
基金资助:
The research of the paper was supported by the National Natural Science Foundation of China (nos. 11931010, 11871047), by the key research project of Academy for Multidisciplinary Studies, Capital Normal University, and by the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds (no. 007/20530290068).

Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

Fangfang Hao¹, Hai-Liang Li^1,2, Luyao Shang¹, Shuang Zhao^1,2

1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;
2. Academy for Multidisciplinary Studies, Capital Normal University, Beijing, 100048, China

Received:2021-12-16 Revised:2022-03-21 Online:2023-09-20 Published:2023-08-29
Contact: Shuang Zhao,E-mail:shuangzhaomath@163.com E-mail:shuangzhaomath@163.com
Supported by:
The research of the paper was supported by the National Natural Science Foundation of China (nos. 11931010, 11871047), by the key research project of Academy for Multidisciplinary Studies, Capital Normal University, and by the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds (no. 007/20530290068).

摘要/Abstract

摘要： According to the boundary condition with the zero, negative, or positive velocity, the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three cases: impermeable problem, inflow problem, or outflow problem. In this paper, we review the recent progress on the existence and nonlinear stability of the stationary solution to the outflow/inflow problems for viscous multi-phase flow.

关键词: Two-phase flow, Outflow/inflow problem, Stationary solution, Navier-Stokes equations

Abstract: According to the boundary condition with the zero, negative, or positive velocity, the initial boundary problem for compressible multi-phase flow with the Dirichlet-type boundary condition can be classified into three cases: impermeable problem, inflow problem, or outflow problem. In this paper, we review the recent progress on the existence and nonlinear stability of the stationary solution to the outflow/inflow problems for viscous multi-phase flow.

Key words: Two-phase flow, Outflow/inflow problem, Stationary solution, Navier-Stokes equations

中图分类号:

Fangfang Hao, Hai-Liang Li, Luyao Shang, Shuang Zhao. Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow[J]. Communications on Applied Mathematics and Computation, 2023, 5(3): 987-1014.

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Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow

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