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

Fangfang Hao; Hai-Liang Li; Luyao Shang; Shuang Zhao

doi:10.1007/s42967-022-00194-1

Communications on Applied Mathematics and Computation ›› 2022, Vol. 5 ›› Issue (3) : 987-1014. DOI: 10.1007/s42967-022-00194-1

Review Article

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

Fangfang Hao¹ ,
Hai-Liang Li¹^,² ,
Luyao Shang¹ ,
Shuang Zhao¹^,²^,d

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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.

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Fangfang Hao, Hai-Liang Li, Luyao Shang, Shuang Zhao. Recent Progress on Outflow/Inflow Problem for Viscous Multi-phase Flow. Communications on Applied Mathematics and Computation, 2022, 5(3): 987‒1014 https://doi.org/10.1007/s42967-022-00194-1

Funding

National Natural Science Foundation of China(11871047); Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(007/20530290068); key research project of Academy for Multidisciplinary Studies, Capital Normal University