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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 & Continuous Dynamical Systems  A, 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 & Related Models, 2010, 3 (4) : 685728. doi: 10.3934/krm.2010.3.685 
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Yanbo Hu, Tong Li. The regularity of a degenerate Goursat problem for the 2D isothermal Euler equations. Communications on Pure & Applied Analysis, 2019, 18 (6) : 33173336. doi: 10.3934/cpaa.2019149 
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Min Ding, Hairong Yuan. Stability of transonic jets with strong rarefaction waves for twodimensional steady compressible Euler system. Discrete & Continuous Dynamical Systems  A, 2018, 38 (6) : 29112943. doi: 10.3934/dcds.2018125 
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GuiQiang Chen, Jun Chen, Mikhail Feldman. Transonic flows with shocks past curved wedges for the full Euler equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (8) : 41794211. doi: 10.3934/dcds.2016.36.4179 
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Dongbing Zha. Remarks on nonlinear elastic waves in the radial symmetry in 2D. Discrete & Continuous Dynamical Systems  A, 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 & Continuous Dynamical Systems  A, 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 & Continuous Dynamical Systems  A, 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 & 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 & Continuous Dynamical Systems  A, 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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems  B, 2003, 3 (1) : 105144. doi: 10.3934/dcdsb.2003.3.105 
[17] 
Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initialboundary value problem of a 2D KazhikhovSmagulov type model. Discrete & Continuous Dynamical Systems  S, 2014, 7 (5) : 917923. doi: 10.3934/dcdss.2014.7.917 
[18] 
Martina ChirilusBruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267275. doi: 10.3934/proc.2015.0267 
[19] 
Tian Ma, Shouhong Wang. Global structure of 2D incompressible flows. Discrete & Continuous Dynamical Systems  A, 2001, 7 (2) : 431445. doi: 10.3934/dcds.2001.7.431 
[20] 
Nusret Balci, Ciprian Foias, M. S Jolly, Ricardo Rosa. On universal relations in 2D turbulence. Discrete & Continuous Dynamical Systems  A, 2010, 27 (4) : 13271351. doi: 10.3934/dcds.2010.27.1327 
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