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Spherically symmetric Navier-Stokes equations with degenerate viscosity coefficients and vacuum
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$
1. | Department of Mathematics, Shanghai University, Shanghai, 200444, College of Mathematics and System Sciences, Urumqi, 830000, Xinjiang, China |
2. | Department of Mathematics, Shanghai University, Shanghai, 200444, China |
3. | Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, China |
[1] |
Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 555-584. doi: 10.3934/dcds.1995.1.555 |
[2] |
Tung Chang, Gui-Qiang Chen, Shuli Yang. On the 2-D Riemann problem for the compressible Euler equations II. Interaction of contact discontinuities. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 419-430. doi: 10.3934/dcds.2000.6.419 |
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Qin Wang, Kyungwoo Song. The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1661-1675. doi: 10.3934/dcds.2016.36.1661 |
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Jianjun Chen, Wancheng Sheng. The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2018, 17 (1) : 127-142. doi: 10.3934/cpaa.2018008 |
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Geng Lai, Wancheng Sheng, Yuxi Zheng. Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 489-523. doi: 10.3934/dcds.2011.31.489 |
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Lihui Guo, Tong Li, Gan Yin. The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. Communications on Pure & Applied Analysis, 2017, 16 (1) : 295-310. doi: 10.3934/cpaa.2017014 |
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Meixiang Huang, Zhi-Qiang Shao. Riemann problem for the relativistic generalized Chaplygin Euler equations. Communications on Pure & Applied Analysis, 2016, 15 (1) : 127-138. doi: 10.3934/cpaa.2016.15.127 |
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Roberto Triggiani. Stability enhancement of a 2-D linear Navier-Stokes channel flow by a 2-D, wall-normal boundary controller. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 279-314. doi: 10.3934/dcdsb.2007.8.279 |
[9] |
Ju Ge, Wancheng Sheng. The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2733-2748. doi: 10.3934/cpaa.2014.13.2733 |
[10] |
Huahui Li, Zhiqiang Shao. Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2373-2400. doi: 10.3934/cpaa.2016041 |
[11] |
Bingbing Ding, Ingo Witt, Huicheng Yin. Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations. Communications on Pure & Applied Analysis, 2017, 16 (3) : 719-744. doi: 10.3934/cpaa.2017035 |
[12] |
Antonio Pumariño, José Ángel Rodríguez, Enrique Vigil. Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 941-966. doi: 10.3934/dcds.2018040 |
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Chuandong Li, Fali Ma, Tingwen Huang. 2-D analysis based iterative learning control for linear discrete-time systems with time delay. Journal of Industrial & Management Optimization, 2011, 7 (1) : 175-181. doi: 10.3934/jimo.2011.7.175 |
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Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917 |
[15] |
Tian Ma, Shouhong Wang. Global structure of 2-D incompressible flows. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 431-445. doi: 10.3934/dcds.2001.7.431 |
[16] |
Jean-françois Coulombel, Paolo Secchi. Uniqueness of 2-D compressible vortex sheets. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1439-1450. doi: 10.3934/cpaa.2009.8.1439 |
[17] |
Nusret Balci, Ciprian Foias, M. S Jolly, Ricardo Rosa. On universal relations in 2-D turbulence. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1327-1351. doi: 10.3934/dcds.2010.27.1327 |
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Oleg Yu. Imanuvilov, Jean Pierre Puel. On global controllability of 2-D Burgers equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 299-313. doi: 10.3934/dcds.2009.23.299 |
[19] |
Yuri N. Fedorov, Luis C. García-Naranjo, Joris Vankerschaver. The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4017-4040. doi: 10.3934/dcds.2013.33.4017 |
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Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi. Stability of the travelling wave in a 2D weakly nonlinear Stefan problem. Kinetic & Related Models, 2009, 2 (1) : 109-134. doi: 10.3934/krm.2009.2.109 |
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