Normal form and global solutions for the Klein-Gordon-Zakharov equations

T. Ozawa; K. Tsutaya; Y. Tsutsumi

Annales de l'I.H.P. Analyse non linéaire (1995)

  • Volume: 12, Issue: 4, page 459-503
  • ISSN: 0294-1449

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Ozawa, T., Tsutaya, K., and Tsutsumi, Y.. "Normal form and global solutions for the Klein-Gordon-Zakharov equations." Annales de l'I.H.P. Analyse non linéaire 12.4 (1995): 459-503. <http://eudml.org/doc/78366>.

@article{Ozawa1995,
author = {Ozawa, T., Tsutaya, K., Tsutsumi, Y.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Cauchy problem; Klein-Gordon-Zakharov equations; small initial data; unique global solutions; method of normal forms},
language = {eng},
number = {4},
pages = {459-503},
publisher = {Gauthier-Villars},
title = {Normal form and global solutions for the Klein-Gordon-Zakharov equations},
url = {http://eudml.org/doc/78366},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Ozawa, T.
AU - Tsutaya, K.
AU - Tsutsumi, Y.
TI - Normal form and global solutions for the Klein-Gordon-Zakharov equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 4
SP - 459
EP - 503
LA - eng
KW - Cauchy problem; Klein-Gordon-Zakharov equations; small initial data; unique global solutions; method of normal forms
UR - http://eudml.org/doc/78366
ER -

References

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  2. [2] J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1976. Zbl0344.46071MR482275
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  4. [4] A. Friedman, Partial Differential Equations, Holt Rinehart and Winston, New York, 1969. Zbl0224.35002MR445088
  5. [5] V. Georgiev, Global solutions of the system of wave and Klein-Gordon equations, Math. Z., Vol. 203, 1990, pp. 683-698. Zbl0671.35052MR1044072
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  8. [8] J. Ginibre and G. Velo, Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 43, 1985, pp. 399-442. Zbl0595.35089MR824083
  9. [9] S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equations, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 321-332. Zbl0635.35059MR784477
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  11. [11] H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., Vol. 185, 1984, pp. 261-270. Zbl0538.35063MR731347
  12. [12] J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 685-696. Zbl0597.35101MR803256
  13. [13] T. Sideris, Decay estimates for the three-dimensional inhomogeneous Klein-Gordon equation and applications, Commun. Part. Diff. Eqs., Vol. 14, 1989, pp. 1421-1455. Zbl0696.35015MR1022992
  14. [14] W.A. Strauss, Nonlinear Wave Equations, CBMS Regional Conference Series in Mathematics, no. 73, Amer. Math. Soc., Providence, RI, 1989. Zbl0714.35003MR1032250
  15. [15] S.G. Thornhill and D. ter Haar, Langmuir turbulence and modulational instability, Phys. Reports (Sect. C of Phys. Lett.), Vol. 43, 1978, pp. 43-99. 
  16. [16] J.C.H. Simon and E. Taflin, The Cauchy problem for non-linear Klein-Gordon equations, Commun. Math. Phys., Vol. 152, 1993, pp. 433-478. Zbl0783.35066MR1213298

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