# American Institute of Mathematical Sciences

• Previous Article
Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients
• KRM Home
• This Issue
• Next Article
Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain
September  2016, 9(3): 455-467. doi: 10.3934/krm.2016003

## Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system

 1 Department of Mathematics, Indiana University, Bloomington, IN 47405 2 Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80002 3 Department of Mathematics Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

Received  September 2015 Revised  January 2016 Published  May 2016

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption of relativistic velocity corrections. The main results are bounds on the spatial and velocity supports of the particle distribution function and uniform estimates on derivatives of this function away from the critical velocity $\vert v_1 \vert = 1$. Additionally, for initial particle distributions that are even in the second velocity argument $v_2$, the global-in-time existence of solutions is shown.
Citation: 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
##### References:

show all references

##### References:
 [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] 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. 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] 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 [5] Etienne Bernard, Laurent Desvillettes, Franç cois Golse, Valeria Ricci. A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures. Kinetic & Related Models, 2018, 11 (1) : 43-69. doi: 10.3934/krm.2018003 [6] 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 [7] 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 [8] Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867 [9] Victor Wasiolek. Uniform global existence and convergence of Euler-Maxwell systems with small parameters. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2007-2021. doi: 10.3934/cpaa.2016025 [10] Marion Acheritogaray, Pierre Degond, Amic Frouvelle, Jian-Guo Liu. Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system. Kinetic & Related Models, 2011, 4 (4) : 901-918. doi: 10.3934/krm.2011.4.901 [11] Miroslav Grmela, Michal Pavelka. Landau damping in the multiscale Vlasov theory. Kinetic & Related Models, 2018, 11 (3) : 521-545. doi: 10.3934/krm.2018023 [12] Hyung Ju Hwang, Jaewoo Jung, Juan J. L. Velázquez. On global existence of classical solutions for the Vlasov-Poisson system in convex bounded domains. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 723-737. doi: 10.3934/dcds.2013.33.723 [13] Bingkang Huang, Lan Zhang. A global existence of classical solutions to the two-dimensional Vlasov-Fokker-Planck and magnetohydrodynamics equations with large initial data. Kinetic & Related Models, 2019, 12 (2) : 357-396. doi: 10.3934/krm.2019016 [14] Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci. Collisionless kinetic theory of rolling molecules. Kinetic & Related Models, 2013, 6 (2) : 429-458. doi: 10.3934/krm.2013.6.429 [15] Emmanuel Frénod, Mathieu Lutz. On the Geometrical Gyro-Kinetic theory. Kinetic & Related Models, 2014, 7 (4) : 621-659. doi: 10.3934/krm.2014.7.621 [16] 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 [17] 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 [18] Jörg Weber. Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020040 [19] Ugo Bessi. Viscous Aubry-Mather theory and the Vlasov equation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 379-420. doi: 10.3934/dcds.2014.34.379 [20] Seung-Yeal Ha, Bingkang Huang, Qinghua Xiao, Xiongtao Zhang. A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data. Communications on Pure & Applied Analysis, 2020, 19 (2) : 835-882. doi: 10.3934/cpaa.2020039

2019 Impact Factor: 1.311