American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields
  • CPAA Home
  • This Issue
  • Next Article
    Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems
March  2002, 1(1): 103-125. doi: 10.3934/cpaa.2002.1.103

A new approach to study the Vlasov-Maxwell system

Sergiu Klainerman 1, and  Gigliola Staffilani 2,

1. 

Princeton University, United States
2. 

Stanford University, United States

Received  July 2001 Published  December 2001

We give a new proof based on Fourier Transform of the classical Glassey and Strauss [6] global existence result for the 3D relativistic Vlasov-Maxwell system, under the assumption of compactly supported particle densities. Though our proof is not substantially shorter than that of [6], we believe it adds a new perspective to the problem. In particular the proof is based on three main observations, see Facts 1-3 following the statement of Theorem 1.4, which are of independent interest.
Keywords: Vlasov-Maxwell system.
Mathematics Subject Classification: 65Mxx.
Citation: 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
[1]

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
[2]

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
[3]

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
[4]

Yemin Chen. Smoothness of classical solutions to the Vlasov-Maxwell-Landau system near Maxwellians. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 889-910. doi: 10.3934/dcds.2008.20.889
[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]

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
[8]

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
[9]

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
[10]

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
[11]

Katherine Zhiyuan Zhang. Focusing solutions of the Vlasov-Poisson system. Kinetic & Related Models, 2019, 12 (6) : 1313-1327. doi: 10.3934/krm.2019051
[12]

Jiann-Sheng Jiang, Chi-Kun Lin, Chi-Hua Liu. Homogenization of the Maxwell's system for conducting media. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 91-107. doi: 10.3934/dcdsb.2008.10.91
[13]

Frank Jochmann. Decay of the polarization field in a Maxwell Bloch system. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 663-676. doi: 10.3934/dcds.2003.9.663
[14]

Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020036
[15]

Robert T. Glassey, Walter A. Strauss. Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 457-472. doi: 10.3934/dcds.1999.5.457
[16]

Ling Hsiao, Fucai Li, Shu Wang. Combined quasineutral and inviscid limit of the Vlasov-Poisson-Fokker-Planck system. Communications on Pure & Applied Analysis, 2008, 7 (3) : 579-589. doi: 10.3934/cpaa.2008.7.579
[17]

Blanca Ayuso, José A. Carrillo, Chi-Wang Shu. Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. Kinetic & Related Models, 2011, 4 (4) : 955-989. doi: 10.3934/krm.2011.4.955
[18]

Jack Schaeffer. Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior. Kinetic & Related Models, 2012, 5 (1) : 129-153. doi: 10.3934/krm.2012.5.129
[19]

Gianluca Crippa, Silvia Ligabue, Chiara Saffirio. Lagrangian solutions to the Vlasov-Poisson system with a point charge. Kinetic & Related Models, 2018, 11 (6) : 1277-1299. doi: 10.3934/krm.2018050
[20]

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

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences