Hostname: page-component-7b9c58cd5d-bslzr Total loading time: 0.001 Render date: 2025-03-15T15:48:06.968Z Has data issue: false hasContentIssue false
  • English
  • Français

An Euler-Poisson system in plasmas

Published online by Cambridge University Press:  17 February 2009

A. Nouri
A. Nouri
Affiliation:
Insa, 20 av A Einstein, 69621 Villeurbanne Cedex, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A local existence and uniqueness result is proved for the three-dimensional Euler-Poisson system without a pressure term which arises in plasma physics.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 4 , April 2000 , pp. 442 - 450
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Bouchut, F., “On zero pressure gas dynamics”, in Advances in kinetic theory and computing selected papers, Series on Advances in Mathematics for Applied Sciences 22, (World Scientific, Singapore, 1994) 171–190.CrossRefGoogle Scholar
[2]Brenier, Y., Grenier, E., “Sticky particles and scalar conservation laws”, SIAM J. Num. Anal. 35 (1998) 2317–2328.CrossRefGoogle Scholar
[3]Forestier, A. and Le Floch, P., “Multivalued solutions to some non-linear and non-strictly hyperbolic systems”, Japan J. Indust. Appl. Math. 9 (1992) 1–23.CrossRefGoogle Scholar
[4]Hartman, P. and Wintner, A., “On hyperbolic partial differential equations”, Amer. J. Math. 74 (1952) 834–864.CrossRefGoogle Scholar
[5]Hörmander, L., “The lifespan of classical solutions of non-linear hyperbolic equations”, 1985, Report no 5.Google Scholar
[6]Lax, P., “Hyperbolic systems of conservation laws”, Comm. Pure Appl. Math. 10 (1957) 537–566.CrossRefGoogle Scholar
[7]Majda, A., Compressible fluid flow and systems of conservation laws in several space variables (Springer, 1984).CrossRefGoogle Scholar
[8]Nouri, A., “Paraxial approximation of Vlasov-Maxwell system: Laminar beams”, M3AS 4 (1994) 203–221.Google Scholar
[9]Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, 1970).Google Scholar
[10]Wagner, D. H., “Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions”, J. Differential Eqns. 68 (1987) 118–136.CrossRefGoogle Scholar
[11]Weinberger, H. F. and Protter, M. H., Maximum principles in differential equations (Prentice-Hall, Inc., 1967).Google Scholar