Derivation of the Zakharov equations

Benjamin Texier[1]

  • [1] Indiana University, Bloomington, IN 47405

Journées Équations aux dérivées partielles (2005)

  • page 1-13
  • ISSN: 0752-0360

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Texier, Benjamin. "Derivation of the Zakharov equations." Journées Équations aux dérivées partielles (2005): 1-13. <http://eudml.org/doc/10607>.

@article{Texier2005,
affiliation = {Indiana University, Bloomington, IN 47405},
author = {Texier, Benjamin},
journal = {Journées Équations aux dérivées partielles},
keywords = {Euler-Maxwell equations; pseudo-differential changes of variables; Zakharov equations; approximation solution; Sobolev estimates},
language = {eng},
month = {6},
pages = {1-13},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Derivation of the Zakharov equations},
url = {http://eudml.org/doc/10607},
year = {2005},
}

TY - JOUR
AU - Texier, Benjamin
TI - Derivation of the Zakharov equations
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 13
LA - eng
KW - Euler-Maxwell equations; pseudo-differential changes of variables; Zakharov equations; approximation solution; Sobolev estimates
UR - http://eudml.org/doc/10607
ER -

References

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  2. T. Colin, G. Ebrard, G. Gallice, B. Texier, Justification of the Zakharov model from Klein-Gordon-waves systems, Comm. Partial Diff. Eq. 29 (2004), no. 9-10, 1365-1401. Zbl1063.35111MR2103840
  3. T. Colin, G. Métivier, in preparation. 
  4. E. Grenier, Pseudo-differential estimates of singular perturbations, Comm. Pure and Applied Math., vol. 50 (1997), 821-865. Zbl0884.35183MR1459589
  5. J.-L. Joly, G. Métivier, J. Rauch, Transparent nonlinear geometric optics and Maxwell-Bloch equations, J. Diff. Eq., vol. 166 (2000), 175-250. Zbl1170.78311MR1779260
  6. D. Lannes, Sharp estimates for pseudo-differential operators with limited regularity and commutators, submitted. Zbl1099.35191
  7. F. Linares, A. Ponce, J. C. Saut, On a degenerate Zakharov system, Bull. Braz. Math. Soc. 36 (2005), no. 1, 1-23. Zbl1070.35087
  8. G. Métivier, K. Zumbrun, Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems, Mem. Amer. Math. Soc., vol. 175, no. 826 (2005). Zbl1074.35066MR2130346
  9. T. Ozawa, Y. Tsutsumi, Existence and smoothing effect of solution for the Zakharov equation, Publ. Res. Inst. Math. Sci., vol. 28, no. 3 (1992), 329-361. Zbl0842.35116MR1184829
  10. S. Schochet, M. Weinstein, The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence, Comm. Math. Physics, vol. 106 (1986), 569-580. Zbl0639.76054MR860310
  11. M. Taylor, Pseudodifferential operators and nonlinear PDE, Progress in Mathematics vol. 100, Birkhaüser Boston, 1991. Zbl0746.35062MR1121019
  12. B. Texier, WKB asymptotics for the Euler-Maxwell equations, Asymptotic Analysis 42 (2005), no. 3-4, 211-250. Zbl1116.35114MR2138794
  13. B. Texier, Derivation of the Zakharov equations, submitted. Zbl05146096
  14. S. Musher, A. Rubenchik, V. Zakharov , Hamiltonian approach to the description of nonlinear plasma phenomena, Phys. Reports, vol. 129 (1985), 285-366. MR824169

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