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On incompressible limits for the NavierStokes system on unbounded domains under slip boundary conditions
On the relevance of the dam break problem in the context of nonlinear shallow water equations
1.  Université de Savoie, CNRSLAMA, Campus Scientifique, 73376 Le BourgetduLac, France 
2.  UMR de Mathématiques, Université de ParisSud, Bâtiment 425, P.O. Box, 91405 Orsay, France 
[1] 
Stefan Berres, Ricardo RuizBaier, Hartmut Schwandt, Elmer M. Tory. An adaptive finitevolume method for a model of twophase pedestrian flow. Networks & Heterogeneous Media, 2011, 6 (3) : 401423. doi: 10.3934/nhm.2011.6.401 
[2] 
Changyan Li, Hui Li. Wellposedness of the twophase flow problem in incompressible MHD. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 56095632. doi: 10.3934/dcds.2021090 
[3] 
Theodore Tachim Medjo. A twophase flow model with delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (9) : 32733294. doi: 10.3934/dcdsb.2017137 
[4] 
G. Deugoué, B. Jidjou Moghomye, T. Tachim Medjo. Approximation of a stochastic twophase flow model by a splittingup method. Communications on Pure & Applied Analysis, 2021, 20 (3) : 11351170. doi: 10.3934/cpaa.2021010 
[5] 
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete & Continuous Dynamical Systems  B, 2010, 13 (3) : 593608. doi: 10.3934/dcdsb.2010.13.593 
[6] 
Marie Henry, Danielle Hilhorst, Robert Eymard. Singular limit of a twophase flow problem in porous medium as the air viscosity tends to zero. Discrete & Continuous Dynamical Systems  S, 2012, 5 (1) : 93113. doi: 10.3934/dcdss.2012.5.93 
[7] 
Zhen Cheng, Wenjun Wang. The Cauchy problem of a twophase flow model for a mixture of noninteracting compressible fluids. Communications on Pure & Applied Analysis, 2021, 20 (12) : 41554176. doi: 10.3934/cpaa.2021151 
[8] 
T. Tachim Medjo. Averaging of an homogeneous twophase flow model with oscillating external forces. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 36653690. doi: 10.3934/dcds.2012.32.3665 
[9] 
Esther S. Daus, JosipaPina Milišić, Nicola Zamponi. Global existence for a twophase flow model with crossdiffusion. Discrete & Continuous Dynamical Systems  B, 2020, 25 (3) : 957979. doi: 10.3934/dcdsb.2019198 
[10] 
Theodore TachimMedjo. Optimal control of a twophase flow model with state constraints. Mathematical Control & Related Fields, 2016, 6 (2) : 335362. doi: 10.3934/mcrf.2016006 
[11] 
Nora Aïssiouene, MarieOdile Bristeau, Edwige Godlewski, Jacques SainteMarie. A combined finite volume  finite element scheme for a dispersive shallow water system. Networks & Heterogeneous Media, 2016, 11 (1) : 127. doi: 10.3934/nhm.2016.11.1 
[12] 
Madalina Petcu, Roger Temam. An interface problem: The twolayer shallow water equations. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 53275345. doi: 10.3934/dcds.2013.33.5327 
[13] 
Feng Ma, Mingfang Ni. A twophase method for multidimensional number partitioning problem. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 203206. doi: 10.3934/naco.2013.3.203 
[14] 
Barbara Lee Keyfitz, Richard Sanders, Michael Sever. Lack of hyperbolicity in the twofluid model for twophase incompressible flow. Discrete & Continuous Dynamical Systems  B, 2003, 3 (4) : 541563. doi: 10.3934/dcdsb.2003.3.541 
[15] 
K. Domelevo. Wellposedness of a kinetic model of dispersed twophase flow with pointparticles and stability of travelling waves. Discrete & Continuous Dynamical Systems  B, 2002, 2 (4) : 591607. doi: 10.3934/dcdsb.2002.2.591 
[16] 
Yangyang Qiao, Huanyao Wen, Steinar Evje. Compressible and viscous twophase flow in porous media based on mixture theory formulation. Networks & Heterogeneous Media, 2019, 14 (3) : 489536. doi: 10.3934/nhm.2019020 
[17] 
Feimin Huang, Dehua Wang, Difan Yuan. Nonlinear stability and existence of vortex sheets for inviscid liquidgas twophase flow. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 35353575. doi: 10.3934/dcds.2019146 
[18] 
Guochun Wu, Yinghui Zhang. Global analysis of strong solutions for the viscous liquidgas twophase flow model in a bounded domain. Discrete & Continuous Dynamical Systems  B, 2018, 23 (4) : 14111429. doi: 10.3934/dcdsb.2018157 
[19] 
Helmut Abels, Harald Garcke, Josef Weber. Existence of weak solutions for a diffuse interface model for twophase flow with surfactants. Communications on Pure & Applied Analysis, 2019, 18 (1) : 195225. doi: 10.3934/cpaa.2019011 
[20] 
Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski. An improved homogenization result for immiscible compressible twophase flow in porous media. Networks & Heterogeneous Media, 2017, 12 (1) : 147171. doi: 10.3934/nhm.2017006 
2020 Impact Factor: 1.327
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