American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On small oscillations of mechanical systems with time-dependent kinetic and potential energy
  • DCDS Home
  • This Issue
  • Next Article
    Optimal Lyapunov inequalities for disfocality and Neumann boundary conditions using $L^p$ norms
October  2008, 20(4): 889-910. doi: 10.3934/dcds.2008.20.889

Smoothness of classical solutions to the Vlasov-Maxwell-Landau system near Maxwellians

Yemin Chen 1,

1. 

Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received  April 2007 Revised  November 2007 Published  January 2008

In this paper we prove that under the assumption that the electromagnetic field is smooth initially, even if the distribution function is not smooth initially, the classical solutions (both the distribution function and the electromagnetic field) to the Vlasov-Maxwell-Landau system become immediately smooth with respect to all variables.
Keywords: Smoothness, averaging lemmas., Vlasov-Maxwell-Landau system.
Mathematics Subject Classification: Primary: 35B65; Secondary: 35Q60, 82D1.
Citation: Yemin Chen. Smoothness of classical solutions to the Vlasov-Maxwell-Landau system near Maxwellians. Discrete & Continuous Dynamical Systems, 2008, 20 (4) : 889-910. doi: 10.3934/dcds.2008.20.889
[1]

Yemin Chen. Smoothness of classical solutions to the Vlasov-Poisson-Landau system. Kinetic & Related Models, 2008, 1 (3) : 369-386. doi: 10.3934/krm.2008.1.369
[2]

Sergiu Klainerman, Gigliola Staffilani. A new approach to study the Vlasov-Maxwell system. Communications on Pure & Applied Analysis, 2002, 1 (1) : 103-125. doi: 10.3934/cpaa.2002.1.103
[3]

Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss. Global magnetic confinement for the 1.5D Vlasov-Maxwell system. Kinetic & Related Models, 2015, 8 (1) : 153-168. doi: 10.3934/krm.2015.8.153
[4]

Jörg Weber. Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder. Kinetic & Related Models, 2020, 13 (6) : 1135-1161. doi: 10.3934/krm.2020040
[5]

Shuangqian Liu, Qinghua Xiao. The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. Kinetic & Related Models, 2016, 9 (3) : 515-550. doi: 10.3934/krm.2016005
[6]

Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials. Kinetic & Related Models, 2013, 6 (1) : 159-204. doi: 10.3934/krm.2013.6.159
[7]

Mohammad Asadzadeh, Piotr Kowalczyk, Christoffer Standar. On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system. Kinetic & Related Models, 2019, 12 (1) : 105-131. doi: 10.3934/krm.2019005
[8]

Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss. Erratum to: Global magnetic confinement for the 1.5D Vlasov-Maxwell system. Kinetic & Related Models, 2015, 8 (3) : 615-616. doi: 10.3934/krm.2015.8.615
[9]

Robert Glassey, Stephen Pankavich, Jack Schaeffer. Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system. Kinetic & Related Models, 2016, 9 (3) : 455-467. doi: 10.3934/krm.2016003
[10]

Yuanjie Lei, Huijiang Zhao. The Vlasov-Maxwell-Boltzmann system near Maxwellians with strong background magnetic field. Kinetic & Related Models, 2020, 13 (3) : 599-621. doi: 10.3934/krm.2020020
[11]

Stephen Pankavich, Nicholas Michalowski. Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system. Kinetic & Related Models, 2015, 8 (1) : 169-199. doi: 10.3934/krm.2015.8.169
[12]

Mihai Bostan, Thierry Goudon. Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case. Kinetic & Related Models, 2008, 1 (1) : 139-170. doi: 10.3934/krm.2008.1.139
[13]

Jin Woo Jang, Robert M. Strain, Tak Kwong Wong. Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021039
[14]

Miroslav Grmela, Michal Pavelka. Landau damping in the multiscale Vlasov theory. Kinetic & Related Models, 2018, 11 (3) : 521-545. doi: 10.3934/krm.2018023
[15]

Yuanjie Lei, Linjie Xiong, Huijiang Zhao. One-species Vlasov-Poisson-Landau system near Maxwellians in the whole space. Kinetic & Related Models, 2014, 7 (3) : 551-590. doi: 10.3934/krm.2014.7.551
[16]

Hai-Liang Li, Hongjun Yu, Mingying Zhong. Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system. Kinetic & Related Models, 2017, 10 (4) : 1089-1125. doi: 10.3934/krm.2017043
[17]

Yunbai Cao, Chanwoo Kim. Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021034
[18]

Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867
[19]

Giuseppe Viglialoro, Thomas E. Woolley. Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3023-3045. doi: 10.3934/dcdsb.2017199
[20]

J. J. Morgan, Hong-Ming Yin. On Maxwell's system with a thermal effect. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 485-494. doi: 10.3934/dcdsb.2001.1.485

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy