ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

doi:10.1007/s10473-022-0104-1

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 91-104.doi: 10.1007/s10473-022-0104-1

ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

麻雅娴¹, 张显文²

1. School of Science, North University of China, Taiyuan, 030051, China;
2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

收稿日期:2020-08-30 修回日期:2021-05-24 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Xianwen ZHANG,E-mail:xwzhang@hust.edu.cn E-mail:xwzhang@hust.edu.cn
作者简介:Yaxian MA,E-mail:myxyxx1994@163.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11871024).

ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

Yaxian MA¹, Xianwen ZHANG²

1. School of Science, North University of China, Taiyuan, 030051, China;
2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

Received:2020-08-30 Revised:2021-05-24 Online:2022-02-25 Published:2022-02-24
Contact: Xianwen ZHANG,E-mail:xwzhang@hust.edu.cn E-mail:xwzhang@hust.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (11871024).

摘要/Abstract

摘要： We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions. For any smooth solution with compact support, we prove a sub-linear growth estimate of its velocity support. As a consequence, we derive some new estimates of the charge densities and the electrostatic field in this situation.

关键词: Vlasov-Poisson system, radiation damping, asymptotic behavior, velocity support

Abstract: We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions. For any smooth solution with compact support, we prove a sub-linear growth estimate of its velocity support. As a consequence, we derive some new estimates of the charge densities and the electrostatic field in this situation.

Key words: Vlasov-Poisson system, radiation damping, asymptotic behavior, velocity support

中图分类号:

35Q83

麻雅娴, 张显文. ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING[J]. 数学物理学报(英文版), 2022, 42(1): 91-104.

Yaxian MA, Xianwen ZHANG. ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING[J]. Acta mathematica scientia,Series B, 2022, 42(1): 91-104.

参考文献

[1] 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
[2] Chen J, Zhang X W, Gao R. Existence, uniqueness and asymptotic behavior for the Vlasov-Poisson system with radiation damping. Acta Math Sin, 2017, 33(5):635-656
[3] Chen Z L, Li X T. Asymptotic growth of support and uniform decay of moments for the Vlasov-Poisson system. SIAM J Math Anal, 2018, 50(4):4180-4202
[4] Chen Z L, Zhang X W. Sub-linear estimate of large velocities in a collisionless plasma. Commun Math Sci, 2014, 12(2):279-291
[5] Chen Z L, Zhang X W. Global existence to the Vlasov-Poisson system and propagation of moments without assumption of finite kinetic energy. Comm Math Phys, 2016, 343(3):851-879
[6] Gasser I, Jabin P E, Perthame B. Regularity and propagation of moments in some nonlinear Vlasov systems. Proc Roy Soc Edinburgh Sect A, 2000, 130(6):1259-1273
[7] Glassey R T. The Cauchy Problem in Kinetic Theory. Philadelphia:Society for Industrial and Applied Mathematics, 1996
[8] Glassey R, Pankavich S, Schaeffer J. Decay in time for a one-dimensional two-component plasma. Math Methods Appl Sci, 2008, 31(18):2115-2132
[9] Horst E. On the asymptotic growth of the solutions of the Vlasov-Poisson system. Math Methods Appl Sci, 1993, 16(2):75-86
[10] Illner R, Rein G. Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case. Math Methods Appl Sci, 1996, 19(17):1409-1413
[11] Kunze M, Rendall A D. Simplified models of electromagnetic and gravitational radiation damping. Classical Quantum Gravity, 2001, 18(17):3573-3587
[12] Kunze M, Rendall A D. The Vlasov-Poisson system with radiation damping. Ann Henri Poincaré, 2001, 2(5):857-886
[13] Lions P L, Perthame B. Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent Math, 1991, 105(2):415-430
[14] Pallard C. A note on the growth of velocities in a collisionless plasma. Math Methods Appl Sci, 2011, 34(7):803-806
[15] Pallard C. Growth estimates and uniform decay for a collisionless plasma. Kinet Relat Models, 2011, 4(2):549-567
[16] Pallard C. Large velocities in a collisionless plasma. J Differential Equations, 2012, 252(3):2864-2876
[17] Pallard C. Moment propagation for weak solutions to the Vlasov-Poisson system. Comm Partial Differential Equations, 2012, 37(7):1273-1285
[18] Pallard C. Space moments of the Vlasov-Poisson system:propagation and regularity. SIAM J Math Anal, 2014, 46(3):1754-1770
[19] Perthame B. Time decay, propagation of low moments and dispersive effects for kinetic equations. Comm Partial Differential Equations, 1996, 21(3/4):659-686
[20] 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
[21] Rein G. Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case. Math Nachr, 1998, 191(1):269-278
[22] Rein G. Collisionless kinetic equation from astrophysics-the Vlasov-Poisson system//Handbook of Differential Equations:Evolutionary Equations. Amsterdam:Elsevier, 2007, 3(383):385-476
[23] Schaeffer J. Asymptotic growth bounds for the Vlasov-Poisson system. Math Methods Appl Sci, 2011, 34(3):262-277
[24] Schaeffer J. On space time estimates for the Vlasov-Poisson system. Math Meth Appl Sci, 2020, 43(7):4075-4085
[25] Xiao M X, Zhang X W. On global solutions to the Vlasov-Poisson system with radiation damping. Kinet Relat Models, 2018, 11(5):1183-1209
[26] Xiao M X, Zhang X W. Moment propagation of the Vlasov-Poisson system with a radiation term. Acta Appl Math, 2019, 160:185-206

ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

ASYMPTOTIC GROWTH BOUNDS FOR THE VLASOV-POISSON SYSTEM WITH RADIATION DAMPING

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 8

[1]	黄浩川, 黄锐. ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CHAFEE-INFANTE EQUATION[J]. 数学物理学报(英文版), 2020, 40(2): 425-441.
[2]	王泽军, 张琦. FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS VIA[J]. 数学物理学报(英文版), 2019, 39(1): 83-93.
[3]	何躏, 廖勇凯, 王涛, 赵会江. ONE-DIMENSIONAL VISCOUS RADIATIVE GAS WITH TEMPERATURE DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2018, 38(5): 1515-1548.
[4]	张建林, 秦玉明. EXACT SOLUTIONS FOR THE CAUCHY PROBLEM TO THE 3D SPHERICALLY SYMMETRIC INCOMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(3): 778-790.
[5]	Kuo-Shou CHIU. ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS[J]. 数学物理学报(英文版), 2018, 38(1): 220-236.
[6]	李杏, 雍燕. LARGE TIME BEHAVIOR OF SOLUTIONS TO 1-DIMENSIONAL BIPOLAR QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS[J]. 数学物理学报(英文版), 2017, 37(3): 806-835.
[7]	Nguyen Tien DUNG. ASYMPTOTIC BEHAVIOR OF LINEAR ADVANCED DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(3): 610-618.
[8]	Zagharide Zine EL ABIDINE. COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL[J]. 数学物理学报(英文版), 2014, 34(5): 1404-1416.
[9]	张映辉, 吴国春. GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING[J]. 数学物理学报(英文版), 2014, 34(2): 424-434.
[10]	陈贵强, 肖长国, 张永前. EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(1): 1-38.
[11]	杨虎, 薛凯. RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS[J]. 数学物理学报(英文版), 2013, 33(4): 998-1006.
[12]	夏莉, 李敬娜, 姚正安. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION[J]. 数学物理学报(英文版), 2012, 32(5): 1875-1882.
[13]	吴舜堂. GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS[J]. 数学物理学报(英文版), 2011, 31(4): 1436-1448.
[14]	杨芬, 张丹丹. SEPARATION PROPERTY OF POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION[J]. 数学物理学报(英文版), 2011, 31(1): 181-193.
[15]	尹景学, 王良伟, 黄锐. COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION[J]. 数学物理学报(英文版), 2010, 30(6): 1865-1880.