Derivation of the Zakharov equations
Texier, Benjamin
Journées équations aux dérivées partielles, (2005), p. 1-13 / Harvested from Numdam
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@article{JEDP_2005____A16_0,
     author = {Texier, Benjamin},
     title = {Derivation of the Zakharov equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2005},
     pages = {1-13},
     doi = {10.5802/jedp.27},
     mrnumber = {2352783},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2005____A16_0}
}

Texier, Benjamin. Derivation of the Zakharov equations. Journées équations aux dérivées partielles,  (2005), pp. 1-13. doi : 10.5802/jedp.27. http://gdmltest.u-ga.fr/item/JEDP_2005____A16_0/

[1] C. Cheverry, O. Guès, G. Métivier, Oscillations fortes sur un champ linéairement dégénéré, Ann. E.N.S., vol. 36, no. 3 (2003.), 691–745 | Numdam | MR 2032985 | Zbl 02128585

[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. | MR 2103840 | Zbl 1063.35111

[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. | MR 1459589 | Zbl 0884.35183

[5] J.-L. Joly, G. Métivier, J. Rauch, Transparent nonlinear geometric optics and Maxwell-Bloch equations, J. Diff. Eq., vol. 166 (2000), 175-250. | MR 1779260 | Zbl 01517171

[6] D. Lannes, Sharp estimates for pseudo-differential operators with limited regularity and commutators, submitted.

[7] F. Linares, A. Ponce, J. C. Saut, On a degenerate Zakharov system, Bull. Braz. Math. Soc. 36 (2005), no. 1, 1-23. | Zbl 1070.35087

[8] G. Métivier, K. Zumbrun, Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems, Mem. Amer. Math. Soc., vol. 175, no. 826 (2005). | MR 2130346 | Zbl 1074.35066

[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. | MR 1184829 | Zbl 0842.35116

[10] S. Schochet, M. Weinstein, The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence, Comm. Math. Physics, vol. 106 (1986), 569-580. | MR 860310 | Zbl 0639.76054

[11] M. Taylor, Pseudodifferential operators and nonlinear PDE, Progress in Mathematics vol. 100, Birkhaüser Boston, 1991. | MR 1121019 | Zbl 0746.35062

[12] B. Texier, WKB asymptotics for the Euler-Maxwell equations, Asymptotic Analysis 42 (2005), no. 3-4, 211-250. | MR 2138794 | Zbl 02190972

[13] B. Texier, Derivation of the Zakharov equations, submitted.

[14] S. Musher, A. Rubenchik, V. Zakharov , Hamiltonian approach to the description of nonlinear plasma phenomena, Phys. Reports, vol. 129 (1985), 285-366. | MR 824169