The relativistic Vlasov-Maxwell system in two space dimensions: Part I

Archive for Rational Mechanics and Analysis

Volumn 141, Issue 4, 1998, Pages 331-354

  Glassey, Robert T ^a   Schaeffer, Jack ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032381779     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050079     Document Type: Article

References (28)

1. ASANO, K. & UKAI, S., On the Vlanov-Poisson Limit of the Vlasov-Maxwell Equation, Patterns and Waves (1986), 369-383.
2. BARDOS, C., DEGOND, P., & NGOAN, H.-T., Existence Globale des solutions des equations de Vlasov-Poisson relativistes en dimension 3, C. R. Acad. Sci. Paris 310, Série I (6) (1985), 265-268.
3. BATT, J., Global Symmetric Solutions of the Initial-Value Problem of Stellar Dynamics, J. Diff. Eqs. 25, (1977), 342-364.
4. BATT, J. & REIN, G., Global Classical Solutions of the Periodic Vlasov-Poisson System in Three Dimensions, C. R. Acad. Sci. Paris 313, Serie I (1991), 411-416.
5. DEGOND, P., Local Existence of Solutions of the Vlasov-Maxwell Equations and Convergence to the Vlasov-Poisson Equations for Infinite Light Velocity, Internal Report No. 117, Centre de Mathématiques Appliquées, Ecole Polytechnique, Paris, Dec. 1984.
6. GLASSEY, R & SCHAEFFER, J., On Symmetric Solutions of the Relativistic Vlasov-Poisson System, Comm. Math. Phys. 101, (1985), 459-473.
7. GLASSEY, R. & SCHAEFFER, J., Control of Velocities Generated in a Two-Dimensional Collisionless Plasma wish Symmetry, Trans. Theory and Stat. Phys. 17 (1988), 467-560.
8. GLASSEY, R. & SCHAEFFER, J., Global Existence of the Relativistic Vlasov-Maxwell System with Nearly Neutral Initial Data, Comm. Math. Phys. 119 (1988), 353-384.
9. GLASSEY, R. & SCHAEFFER, J., On the 'One and One-Half Dimensional Relativistic Vlasov-Maxwell System, Math. Meth. Appl. Sci. 13 (1990), 169-179.
10. GLASSEY, R. & STRAUSS, W., Singularity Formation in a Collisonless Plasma Could Occur Only at High Velocities, Arch. Rational Mech. Anal. 92 (1986), 59-90.
11. GLASSEY, R. & STRAUSS, W., High Velocity Particles in a Collisionless Plasma, Math. Meth. Appl. Sci. 9 (1987), 46-52.
12. GLASSEY, R. & STRAUSS, W., Remarks on Collisionless Plasmas, Contemporary Mathematics 28 (1984), 269-279.
13. GLASSEY, R. & STRAUSS, W., Absence of Shocks in an Initially Dilute Collision-less Plasma, Comm. Math. Phys. 113 (1987), 191-208.
14. HORST, E., On the Classical Solutions of the Initial Value Problem for the Unmodified Nonlinear Vlasov-Equation, Parts I and II, Math. Meth. Appl. Sci. 3 (1981), 229-248;
15. 4 (1982), 19-32.
16. HORST, E., Global Solutions of the Relativistic Vlasov-Maxwell System of Plasma Physics, Habilitationsschrift, Universität München, 1986.
17. HORST, E., On the Asymptotic Growth of the Solutions of the Vlasov-Poisson System, Math. Meth. Appl. Sci. 16 (1993), 75-85.
18. LIONS, P.-L. & DIPERNA, R., Global Solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math. 42 (1989), 729-757.
19. LIONS, P.-L. & PERTHAME, B., Propagation of Moments and Regularity for the Three Dimensional Vlasov-Poisson System, Invent. Math. 105 (1991), 415-430.
20. NEUNZERT, H. & PETRY, K. H., Ein Existenzsatz für die Vlasov-Gleichung mit selbstkonsistentem Magnetfeld, Math. Meth. Appl. Sci. 2 (1980), 429-444.
21. PFAFFELMOSER, K., Global Classical Solution of the Vlasov-Poisson System in Three Dimensions for General Initial Data, J. Diff. Eqs. 95 (1992), 281-303.
22. RAMMAHA, M., Global Solutions of the Two-Dimensional Relativistic Vlasov-Poisson System, Trans. Theory and Stat. Phys. 16 (1987), 61-87.
23. REIN, G., Generic Global Solutions of the Relativistic Vlasov-Maxwell System of Plasma Physics, Comm. Math. Phys. 135 (1990), 41-78.
24. SCHAEFFER, J., The Classical Limit of the Relativistic Vlasov-Maxwell System, Comm. Math. Phys. 104 (1986), 403-421.
25. SCHAEFFER, J., Global Existence of Smooth Solutions to the Vlasov Poisson System in Three Dimensions, Comm. Partial Diff. Eqs. 16 (1991), 1313-1335.
26. UKAI, S. & OKABE, T., On Classical Solutions in the Large in Time of Two-Dimensional Vlasov's Equation, Osaka J. Math. 15 (1978), 245-261.
27. WOLLMAN, S., An Existence and Uniqueness Theorem for the Vlasov-Maxwell System, Comm. Pure Appl. Math. 37 (1984), 457-462.
28. WOLLMAN, S., Global-in-Time Solutions of the Two Dimensional Vlasov-Poisson System, Comm. Pure Appl. Math. 33 (1980), 173-197.