Derivation of the Zakharov equations

  title={Derivation of the Zakharov equations},
  author={Benjamin Texier},
This article continues the study, initiated in [28, 8], of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions… CONTINUE READING
14 Citations
26 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 14 extracted citations


Publications referenced by this paper.
Showing 1-10 of 26 references

Pseudo-differential estimates of singular perturbations

  • E. Grenier
  • Comm. Pure and Applied Math., vol. 50
  • 1997
Highly Influential
5 Excerpts

Existence and smoothing effect of solution for the Zakharov equation

  • T. Ozawa, Y. Tsutsumi
  • Publ. Res. Inst. Math. Sci., vol. 28, no. 3
  • 1992
Highly Influential
6 Excerpts

Sharp estimates for pseudo-differential operators with limited regularity and commutators

  • D. Lannes
  • J. Funct. Analysis 232
  • 2006
Highly Influential
10 Excerpts

WKB asymptotics for the Euler-Maxwell equations

  • B. Texier
  • Asymptotic Analysis 42
  • 2005
Highly Influential
10 Excerpts

Justification of the Zakharov model from Klein-Gordon-waves systems, Comm

  • T. Colin, G. Ebrard, G. Gallice, B. Texier
  • Partial Diff. Eq
  • 2004
Highly Influential
6 Excerpts

Transparent nonlinear geometric optics and Maxwell-Bloch equations

  • J.-L. Joly, G. Métivier, J. Rauch
  • J. Diff. Eq., vol. 166
  • 2000
Highly Influential
5 Excerpts

Quelques résultats de régularité pour les équations de la turbulence de Langmuir

  • C. Sulem, P.-L. Sulem
  • C. R. Acad. Sci. Paris Seŕ. A-B 289
  • 1979
Highly Influential
2 Excerpts

Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems

  • G. Métivier, K. Zumbrun
  • Mem. Amer. Math. Soc., vol. 175, no. 826
  • 2005
2 Excerpts

Similar Papers

Loading similar papers…