Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 668-674.doi: 10.1007/s10473-023-0212-6
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Jingpeng, Wu, Xianwen Zhang†
Received:
2021-12-07
Revised:
2022-03-31
Online:
2023-03-25
Published:
2023-04-12
Contact:
†Xianwen ZHANG, E-mail: About author:
Jingpeng Wu, E-mail: d201980015@hust.edu.cn
Supported by:
Jingpeng, Wu, Xianwen Zhang. THE ENERGY CONSERVATION OF VLASOV-POISSON SYSTEMS*[J].Acta mathematica scientia,Series B, 2023, 43(2): 668-674.
[1] Arsen'ev A A. Existence and uniqueness of the classical solution of Vlasov's system of equations. USSR Comput Math Math Phys, 1975, 15(5): 252-258 [2] Bardos C, Besse N, Nguyen T T.Onsager-type conjecture and renormalized solutions for the relativistic Vlasov-Maxwell system. Quart Appl Math, 2020, 78(2): 193-217 [3] Batt J.Global symmetric solutions of the initial value problem of stellar dynamics. J Differential Equations, 1977, 25(3): 342-364 [4] Castella F.Propagation of space moments in the Vlasov-Poisson equation and further results. Ann Inst H Poincaré Anal Non Linéaire, 1999, 16(4): 503-533 [5] DiPerna R, Lions P L. Solutions globals d'équations du type Vlasov-Poisson (Global solutions of Vlasov- Poisson type equations). C R Acad Sci Paris Series I-Mathematics, 1988, 307(12): 655-658 [6] DiPerna R, Lions P L. Global weak solutions of kinetic equations. Rend Semin Mat Torino, 1988, 46(3): 259-288 [7] Holding T, Miot E.Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces//Danchin R, Farwig R, Neustupa J, Penel P. Mathematical Analysis in Fluid Mechanics-Selected Recent Results. Providence, RI: Amer Math Soc, 2018: 145-162 [8] Horst E, Hunze R.Weak solutions of the initial value problem for the unmodified non-linear Vlasov equation. Math Methods Appl Sci, 1984, 6: 262-279 [9] Kurth R.Das Anfangswertproblem der Stellardynamik. Z Astrophys, 1952, 30: 213-229 [10] Lions P L, Perthame B.Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent Math, 1991, 105(2): 415-430 [11] Loeper G.Uniqueness of the solution to the Vlasov-Poisson system with bounded density. J Math Pures Appl, 2006, 86(1): 68-79 [12] Miot E.A uniqueness criterion for unbounded solutions to the Vlasov-Poisson system. Comm Math Phys, 2016, 346(2): 469-482 [13] Pallard C.Moment propagation for weak solutions to the Vlasov-Poisson system. Comm Partial Differential Equations, 2012, 37(7): 1273-1285 [14] Pallard C.Space moments of the Vlasov-Poisson system: propagation and regularity. SIAM J Math Anal, 2014, 46(3): 1754-1770 [15] Pfaffelmoser K.Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J Differential Equations, 1992, 95(2): 281-303 [16] Rein G.Collisionless kinetic equations from astrophysics-the Vlasov-Poisson system// Dafermos C, Feireisl E. Handbook of Differential Equations: Evolutionary Equations. Amsterdam: Elsevier, 2007: 383-476 [17] Sospedra-Alfonso R.On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell sys- tem. Commun Math Sci, 2010, 8(4): 901-908 [18] Stein E M.Singular Integrals and Differentiability Properties of Functions. Princeton: Princeton University Press, 1970 |
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