-
Previous Article
Hölder-estimates for non-autonomous parabolic problems with rough data
- EECT Home
- This Issue
-
Next Article
The stochastic linear quadratic optimal control problem in Hilbert spaces: A polynomial chaos approach
The energy conservation for weak solutions to the relativistic Nordström-Vlasov system
1. | School of Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China |
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity, Inc. NY, Oxford University Press, 2000. |
[2] |
F. Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Rational Mech. Anal., 157 (2001), 75-90.
doi: 10.1007/PL00004237. |
[3] |
F. Bouchut, F. Golse and C. Pallard, Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system, Rev. Mat.Iberoamericana., 20 (2004), 865-892.
doi: 10.4171/RMI/409. |
[4] |
S. Calogero and G. Rein, Global weak solutions to the Nordström-Vlasov system, J. Differential Equations., 204 (2004), 323-338.
doi: 10.1016/j.jde.2004.02.011. |
[5] |
S. Calogero, Global classical solutions to the 3D Nordström-Vlasov system, Commun. Math. Phys., 266 (2006), 343-353.
doi: 10.1007/s00220-006-0029-x. |
[6] |
S. Calogero, Spherically symmetric steady states of galactic dynamics in scalar gravity, Class. Quantum Grav., 20 (2003), 1729-1741.
doi: 10.1088/0264-9381/20/9/310. |
[7] |
S. Calogero and G. Rein, On classical solutions of the Nordström-Vlasov system, Comm. Partial Diff. Eqs., 28 (2003), 1863-1885.
doi: 10.1081/PDE-120025488. |
[8] |
R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Mxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[9] |
R. J. Diperna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Amer. Math. Soc., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[10] |
L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1998. |
[11] |
S. Friedrich, Global small solutions of the Vlasov-Nordström system, preprint, arXiv:math/0407023v1. |
[12] |
P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[13] |
G. Loeper, Uniqueness of the solution to Vlasov-Poisson system with bounded density, J. Math. Pures Appl., 86 (2006), 68-79.
doi: 10.1016/j.matpur.2006.01.005. |
[14] |
E. Miot, A uniqueness criterion for unbounded solutions to the Vlaosv-Poisson system, arXiv:1409.6988v1. |
[15] |
C. Pallard, On global smooth solutions to the 3D Vlasov-Nordström system, Ann. I. H. Poincaré, 23 (2006), 85-96.
doi: 10.1016/j.anihpc.2005.02.001. |
[16] |
G. Rein, Global weak solutions to the relativistic Vlasov-Maxwell system revisted, Comm. Math. Sci., 2 (2004), 145-158.
doi: 10.4310/CMS.2004.v2.n2.a1. |
[17] |
G. Rein, Collisionless kinetic equation from astrophysics-the Vlasov-Poisson system, in: Handbook of Differential Equations: Evolutionary Equations, {Elsevier}, 3 (2007), 383-476.
doi: 10.1016/S1874-5717(07)80008-9. |
[18] |
R. Sospedra-Alfonso, On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system, Comm. Math. Sci., 8 (2010), 901-908.
doi: 10.4310/CMS.2010.v8.n4.a6. |
[19] |
S. L. Shapiro and S. A. Teukolsky, Scalar gravitation: A laboratory for numerical relativity, Phys. Rev. D., 47 (1993), 1529-1540.
doi: 10.1103/PhysRevD.47.1529. |
show all references
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity, Inc. NY, Oxford University Press, 2000. |
[2] |
F. Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Rational Mech. Anal., 157 (2001), 75-90.
doi: 10.1007/PL00004237. |
[3] |
F. Bouchut, F. Golse and C. Pallard, Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system, Rev. Mat.Iberoamericana., 20 (2004), 865-892.
doi: 10.4171/RMI/409. |
[4] |
S. Calogero and G. Rein, Global weak solutions to the Nordström-Vlasov system, J. Differential Equations., 204 (2004), 323-338.
doi: 10.1016/j.jde.2004.02.011. |
[5] |
S. Calogero, Global classical solutions to the 3D Nordström-Vlasov system, Commun. Math. Phys., 266 (2006), 343-353.
doi: 10.1007/s00220-006-0029-x. |
[6] |
S. Calogero, Spherically symmetric steady states of galactic dynamics in scalar gravity, Class. Quantum Grav., 20 (2003), 1729-1741.
doi: 10.1088/0264-9381/20/9/310. |
[7] |
S. Calogero and G. Rein, On classical solutions of the Nordström-Vlasov system, Comm. Partial Diff. Eqs., 28 (2003), 1863-1885.
doi: 10.1081/PDE-120025488. |
[8] |
R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Mxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[9] |
R. J. Diperna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Amer. Math. Soc., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[10] |
L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1998. |
[11] |
S. Friedrich, Global small solutions of the Vlasov-Nordström system, preprint, arXiv:math/0407023v1. |
[12] |
P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[13] |
G. Loeper, Uniqueness of the solution to Vlasov-Poisson system with bounded density, J. Math. Pures Appl., 86 (2006), 68-79.
doi: 10.1016/j.matpur.2006.01.005. |
[14] |
E. Miot, A uniqueness criterion for unbounded solutions to the Vlaosv-Poisson system, arXiv:1409.6988v1. |
[15] |
C. Pallard, On global smooth solutions to the 3D Vlasov-Nordström system, Ann. I. H. Poincaré, 23 (2006), 85-96.
doi: 10.1016/j.anihpc.2005.02.001. |
[16] |
G. Rein, Global weak solutions to the relativistic Vlasov-Maxwell system revisted, Comm. Math. Sci., 2 (2004), 145-158.
doi: 10.4310/CMS.2004.v2.n2.a1. |
[17] |
G. Rein, Collisionless kinetic equation from astrophysics-the Vlasov-Poisson system, in: Handbook of Differential Equations: Evolutionary Equations, {Elsevier}, 3 (2007), 383-476.
doi: 10.1016/S1874-5717(07)80008-9. |
[18] |
R. Sospedra-Alfonso, On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system, Comm. Math. Sci., 8 (2010), 901-908.
doi: 10.4310/CMS.2010.v8.n4.a6. |
[19] |
S. L. Shapiro and S. A. Teukolsky, Scalar gravitation: A laboratory for numerical relativity, Phys. Rev. D., 47 (1993), 1529-1540.
doi: 10.1103/PhysRevD.47.1529. |
[1] |
Jonathan Ben-Artzi, Stephen Pankavich, Junyong Zhang. A toy model for the relativistic Vlasov-Maxwell system. Kinetic and Related Models, 2022, 15 (3) : 341-354. doi: 10.3934/krm.2021053 |
[2] |
Jörg Weber. Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder. Kinetic and Related Models, 2020, 13 (6) : 1135-1161. doi: 10.3934/krm.2020040 |
[3] |
Lan Luo, Hongjun Yu. Global solutions to the relativistic Vlasov-Poisson-Fokker-Planck system. Kinetic and Related Models, 2016, 9 (2) : 393-405. doi: 10.3934/krm.2016.9.393 |
[4] |
Shuangqian Liu, Qinghua Xiao. The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. Kinetic and Related Models, 2016, 9 (3) : 515-550. doi: 10.3934/krm.2016005 |
[5] |
Dayton Preissl, Christophe Cheverry, Slim Ibrahim. Uniform lifetime for classical solutions to the Hot, Magnetized, Relativistic Vlasov Maxwell system. Kinetic and Related Models, 2021, 14 (6) : 1035-1079. doi: 10.3934/krm.2021042 |
[6] |
Mohammad Asadzadeh, Piotr Kowalczyk, Christoffer Standar. On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system. Kinetic and Related Models, 2019, 12 (1) : 105-131. doi: 10.3934/krm.2019005 |
[7] |
Stephen Pankavich, Nicholas Michalowski. Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system. Kinetic and Related Models, 2015, 8 (1) : 169-199. doi: 10.3934/krm.2015.8.169 |
[8] |
Hai-Liang Li, Hongjun Yu, Mingying Zhong. Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system. Kinetic and Related Models, 2017, 10 (4) : 1089-1125. doi: 10.3934/krm.2017043 |
[9] |
Mihai Bostan, Thierry Goudon. Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case. Kinetic and Related Models, 2008, 1 (1) : 139-170. doi: 10.3934/krm.2008.1.139 |
[10] |
Jin Woo Jang, Robert M. Strain, Tak Kwong Wong. Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus. Kinetic and Related Models, 2022, 15 (4) : 569-604. doi: 10.3934/krm.2021039 |
[11] |
Dequan Yue, Wuyi Yue. Block-partitioning matrix solution of M/M/R/N queueing system with balking, reneging and server breakdowns. Journal of Industrial and Management Optimization, 2009, 5 (3) : 417-430. doi: 10.3934/jimo.2009.5.417 |
[12] |
Meng Wang, Wendong Wang, Zhifei Zhang. On the uniqueness of weak solution for the 2-D Ericksen--Leslie system. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 919-941. doi: 10.3934/dcdsb.2016.21.919 |
[13] |
Yong Zeng. Existence and uniqueness of very weak solution of the MHD type system. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5617-5638. doi: 10.3934/dcds.2020240 |
[14] |
Young-Pil Choi, In-Jee Jeong. Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022021 |
[15] |
Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045 |
[16] |
Philipp Reiter. Regularity theory for the Möbius energy. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1463-1471. doi: 10.3934/cpaa.2010.9.1463 |
[17] |
Robert I. McLachlan, G. R. W. Quispel. Discrete gradient methods have an energy conservation law. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1099-1104. doi: 10.3934/dcds.2014.34.1099 |
[18] |
Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064 |
[19] |
Xuecheng Wang. Decay estimates for the $ 3D $ relativistic and non-relativistic Vlasov-Poisson systems. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022019 |
[20] |
Gianluca Favre, Marlies Pirner, Christian Schmeiser. Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022015 |
2021 Impact Factor: 1.169
Tools
Metrics
Other articles
by authors
[Back to Top]