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BegehrHile operator and its applications to some differential equations
Nonrelativistic global limits to the three dimensional relativistic euler equations with spherical symmetry
1.  Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 
2.  Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 
3.  Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 
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Yachun Li, Xucai Ren. Nonrelativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$law. Communications on Pure & Applied Analysis, 2006, 5 (4) : 963979. doi: 10.3934/cpaa.2006.5.963 
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[3] 
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) : 23732400. doi: 10.3934/cpaa.2016041 
[4] 
Sebastian Bauer. A nonrelativistic model of plasma physics containing a radiation reaction term. Kinetic & Related Models, 2018, 11 (1) : 2542. doi: 10.3934/krm.2018002 
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LaSu Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic EulerPoisson equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 9811004. doi: 10.3934/dcds.2016.36.981 
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Yachun Li, Qiufang Shi. Global existence of the entropy solutions to the isentropic relativistic Euler equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 763778. doi: 10.3934/cpaa.2005.4.763 
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Philippe G. LeFloch, Seiji Ukai. A symmetrization of the relativistic Euler equations with several spatial variables. Kinetic & Related Models, 2009, 2 (2) : 275292. doi: 10.3934/krm.2009.2.275 
[8] 
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 
[9] 
Yongcai Geng. Singularity formation for relativistic Euler and EulerPoisson equations with repulsive force. Communications on Pure & Applied Analysis, 2015, 14 (2) : 549564. doi: 10.3934/cpaa.2015.14.549 
[10] 
Jifeng Chu, Zaitao Liang, Fangfang Liao, Shiping Lu. Existence and stability of periodic solutions for relativistic singular equations. Communications on Pure & Applied Analysis, 2017, 16 (2) : 591609. doi: 10.3934/cpaa.2017029 
[11] 
Yonggeun Cho, Tohru Ozawa. On radial solutions of semirelativistic Hartree equations. Discrete & Continuous Dynamical Systems  S, 2008, 1 (1) : 7182. doi: 10.3934/dcdss.2008.1.71 
[12] 
Xiuting Li. The energy conservation for weak solutions to the relativistic NordströmVlasov system. Evolution Equations & Control Theory, 2016, 5 (1) : 135145. doi: 10.3934/eect.2016.5.135 
[13] 
Thomas Leroy. Relativistic transfer equations: Comparison principle and convergence to the nonequilibrium regime. Kinetic & Related Models, 2015, 8 (4) : 725763. doi: 10.3934/krm.2015.8.725 
[14] 
GuiQiang G. Chen, Hairong Yuan. Local uniqueness of steady spherical transonic shockfronts for the threedimensional full Euler equations. Communications on Pure & Applied Analysis, 2013, 12 (6) : 25152542. doi: 10.3934/cpaa.2013.12.2515 
[15] 
David L. Finn. Convexity of level curves for solutions to semilinear elliptic equations. Communications on Pure & Applied Analysis, 2008, 7 (6) : 13351343. doi: 10.3934/cpaa.2008.7.1335 
[16] 
Marcelo M. Disconzi. On the existence of solutions and causality for relativistic viscous conformal fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 15671599. doi: 10.3934/cpaa.2019075 
[17] 
Juan Calvo. On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state. Communications on Pure & Applied Analysis, 2013, 12 (3) : 13411347. doi: 10.3934/cpaa.2013.12.1341 
[18] 
Philip Korman. Curves of equiharmonic solutions, and problems at resonance. Discrete & Continuous Dynamical Systems  A, 2014, 34 (7) : 28472860. doi: 10.3934/dcds.2014.34.2847 
[19] 
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 
[20] 
Lan Luo, Hongjun Yu. Global solutions to the relativistic VlasovPoissonFokkerPlanck system. Kinetic & Related Models, 2016, 9 (2) : 393405. doi: 10.3934/krm.2016.9.393 
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