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On the 2D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves
1.  Institute of Mathematics, Academia Sinica, Beijing 100080 
2.  Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 602082730 
3.  Institute of Applied Mathematics, Academia Sinica, Beijing 100080 
[1] 
Tung Chang, GuiQiang Chen, Shuli Yang. On the 2D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 419430. doi: 10.3934/dcds.2000.6.419 
[2] 
Feimin Huang, Yi Wang, Tong Yang. Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity. Kinetic and Related Models, 2010, 3 (4) : 685728. doi: 10.3934/krm.2010.3.685 
[3] 
Yanbo Hu, Tong Li. The regularity of a degenerate Goursat problem for the 2D isothermal Euler equations. Communications on Pure and Applied Analysis, 2019, 18 (6) : 33173336. doi: 10.3934/cpaa.2019149 
[4] 
Min Ding, Hairong Yuan. Stability of transonic jets with strong rarefaction waves for twodimensional steady compressible Euler system. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 29112943. doi: 10.3934/dcds.2018125 
[5] 
GuiQiang Chen, Jun Chen, Mikhail Feldman. Transonic flows with shocks past curved wedges for the full Euler equations. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 41794211. doi: 10.3934/dcds.2016.36.4179 
[6] 
Dongbing Zha. Remarks on nonlinear elastic waves in the radial symmetry in 2D. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 40514062. doi: 10.3934/dcds.2016.36.4051 
[7] 
José R. Quintero. Nonlinear stability of solitary waves for a 2d BenneyLuke equation. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 203218. doi: 10.3934/dcds.2005.13.203 
[8] 
Thomas Y. Hou, Danping Yang, Hongyu Ran. Multiscale analysis in Lagrangian formulation for the 2D incompressible Euler equation. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 11531186. doi: 10.3934/dcds.2005.13.1153 
[9] 
Meixiang Huang, ZhiQiang Shao. Riemann problem for the relativistic generalized Chaplygin Euler equations. Communications on Pure and Applied Analysis, 2016, 15 (1) : 127138. doi: 10.3934/cpaa.2016.15.127 
[10] 
Tong Yang, Huijiang Zhao. Asymptotics toward strong rarefaction waves for $2\times 2$ systems of viscous conservation laws. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 251282. doi: 10.3934/dcds.2005.12.251 
[11] 
Harish S. Bhat, Razvan C. Fetecau. Lagrangian averaging for the 1D compressible Euler equations. Discrete and Continuous Dynamical Systems  B, 2006, 6 (5) : 9791000. doi: 10.3934/dcdsb.2006.6.979 
[12] 
Feng Xie. Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model. Discrete and Continuous Dynamical Systems  B, 2012, 17 (3) : 10751100. doi: 10.3934/dcdsb.2012.17.1075 
[13] 
Christian Rohde, Wenjun Wang, Feng Xie. Hyperbolichyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis, 2013, 12 (5) : 21452171. doi: 10.3934/cpaa.2013.12.2145 
[14] 
Gianluca Crippa, Elizaveta Semenova, Stefano Spirito. Strong continuity for the 2D Euler equations. Kinetic and Related Models, 2015, 8 (4) : 685689. doi: 10.3934/krm.2015.8.685 
[15] 
Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible NavierStokes equations with temperature and density dependent transport coefficients. Kinetic and Related Models, 2016, 9 (3) : 469514. doi: 10.3934/krm.2016004 
[16] 
Gero Friesecke, Karsten Matthies. Geometric solitary waves in a 2D massspring lattice. Discrete and Continuous Dynamical Systems  B, 2003, 3 (1) : 105114. doi: 10.3934/dcdsb.2003.3.105 
[17] 
Martina ChirilusBruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267275. doi: 10.3934/proc.2015.0267 
[18] 
Brian Straughan. Shocks and acceleration waves in modern continuum mechanics and in social systems. Evolution Equations and Control Theory, 2014, 3 (3) : 541555. doi: 10.3934/eect.2014.3.541 
[19] 
Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initialboundary value problem of a 2D KazhikhovSmagulov type model. Discrete and Continuous Dynamical Systems  S, 2014, 7 (5) : 917923. doi: 10.3934/dcdss.2014.7.917 
[20] 
Gianmarco Manzini, Annamaria Mazzia. A virtual element generalization on polygonal meshes of the ScottVogelius finite element method for the 2D Stokes problem. Journal of Computational Dynamics, 2022, 9 (2) : 207238. doi: 10.3934/jcd.2021020 
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