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On the 2-D 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 60208-2730 |
3. | Institute of Applied Mathematics, Academia Sinica, Beijing 100080 |
[1] |
Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 419-430. 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) : 685-728. doi: 10.3934/krm.2010.3.685 |
[3] |
Yanbo Hu, Tong Li. The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3317-3336. doi: 10.3934/cpaa.2019149 |
[4] |
Min Ding, Hairong Yuan. Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2911-2943. doi: 10.3934/dcds.2018125 |
[5] |
Gui-Qiang 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) : 4179-4211. doi: 10.3934/dcds.2016.36.4179 |
[6] |
Dongbing Zha. Remarks on nonlinear elastic waves in the radial symmetry in 2-D. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 4051-4062. doi: 10.3934/dcds.2016.36.4051 |
[7] |
José R. Quintero. Nonlinear stability of solitary waves for a 2-d Benney--Luke equation. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 203-218. doi: 10.3934/dcds.2005.13.203 |
[8] |
Thomas Y. Hou, Danping Yang, Hongyu Ran. Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1153-1186. doi: 10.3934/dcds.2005.13.1153 |
[9] |
Meixiang Huang, Zhi-Qiang Shao. Riemann problem for the relativistic generalized Chaplygin Euler equations. Communications on Pure and Applied Analysis, 2016, 15 (1) : 127-138. 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) : 251-282. 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) : 979-1000. 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) : 1075-1100. doi: 10.3934/dcdsb.2012.17.1075 |
[13] |
Christian Rohde, Wenjun Wang, Feng Xie. Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2145-2171. 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) : 685-689. doi: 10.3934/krm.2015.8.685 |
[15] |
Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic and Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004 |
[16] |
Gero Friesecke, Karsten Matthies. Geometric solitary waves in a 2D mass-spring lattice. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 105-114. doi: 10.3934/dcdsb.2003.3.105 |
[17] |
Martina Chirilus-Bruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267-275. 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) : 541-555. doi: 10.3934/eect.2014.3.541 |
[19] |
Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917 |
[20] |
Gianmarco Manzini, Annamaria Mazzia. A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem. Journal of Computational Dynamics, 2022, 9 (2) : 207-238. doi: 10.3934/jcd.2021020 |
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