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2000 | 52 | 1 | 181-188
Tytuł artykułu

On the coupled system of nonlinear wave equations with different propagation speeds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
52
Numer
1
Strony
181-188
Opis fizyczny
Daty
wydano
2000
Twórcy
autor
  • Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
  • Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
  • Mathematical Istitute, Tohoku University, Sendai 980-8578, Japan
Bibliografia
  • [1] D. Bekiranov, T. Ogawa and G. Ponce, Weak solvability and well posedness of the coupled Schrödinger Korteweg-de Vries equations in the capillary-gravity interaction waves, Proc. Amer. Math. Soc. 125 (1997) 2907-2919.
  • [2] D. Bekiranov, T. Ogawa and G. Ponce, Interaction equations for short and long dispersive waves, J. Funct. Anal. 158 (1998) 357-388.
  • [3] J. Bergh and J. Löfström, Interpolation Spaces, An Introduction, Springer-Verlag, Berlin-New York-Heidelberg, 1976.
  • [4] J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear dispersive equations. I Schrödinger equations, Geom. Funct. Anal. 3 (1993) 107-156.
  • [5] J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear dispersive equations. II The KdV equation, Geom. Funct. Anal. 3 (1993) 209-262.
  • [6] J. Bourgain and J. Colliander, On well-posedness of the Zakharov system, Int. Math. Res. Not. 11 (1996) 515-546.
  • [7] R. O. Dendy, Plasma Dynamics, Oxford University Press, Oxford, 1990.
  • [8] J. Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), Séminaire Bourbaki no. 796, Astérisque 237 (1996) 163-187.
  • [9] J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995) 50-68.
  • [10] J. Ginibre, Y. Tsutsumi and G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151 (1997) 384-436.
  • [11] C. E. Kenig, G. Ponce and L. Vega, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J. 71 (1993) 1-21.
  • [12] C. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc. 9 (1996) 573-603.
  • [13] C. Kenig, G. Ponce and L. Vega, Quadratic forms for the 1-D semilinear Schrödinger equation, Trans. Amer. Math. Soc. 348 (1996) 3323-3353.
  • [14] S. Klainerman and M. Machedon, Space time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993) 1221-1268.
  • [15] S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Math. J. 81 (1995) 96-103.
  • [16] S. Klainerman and M. Machedon, Estimates for null forms and the space $H_s,δ$, Int. Math. Res. Not. 17 (1996) 853-365.
  • [17] S. Klainerman and S. Selberg, Remark on the optimal regularity for equations of wave map in 3D, Comm. Part. Diff. Eqs. 22 (1997) 901-918.
  • [18] H. Lindblad, A sharp counterexample to the local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993) 503-539.
  • [19] H. Lindblad, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math. 118 (1996) 1-16.
  • [20] H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995) 357-426.
  • [21] T. Ozawa, K. Tsutaya and Y. Tsutsumi, Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions, Math. Annalen 313 (1999) 127-140.
  • [22] H. Pecher, Nonlinear samll data scattering for the wave and Klein-Gordon equation, Math. Z. 185 (1984) 261-270.
  • [23] G. Ponce and T. Sideris, Local regularity of nonlinear wave equations in three space dimensions, Comm. Part. Diff. Eqs. 18 (1993) 169-177.
  • [24] R. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977) 705-714.
  • [25] K. Tsugawa, Well-posedness in the energy space for the Cauchy problem of the coupled system of complex scalar field and Maxwell equations, to appear in Fukcialaj Ekvacioj.
  • [26] K. Tsutaya, Local regularity of non-resonant nonlinear wave equations, Diff. Integr. Eqns. 11 (1998) 279-292.
  • [27] V. E. Zakharov, Collapse of Langmuir waves, Sov. Phys. JETP 35 (1972) 908-914.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv52z1p181bwm
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