TY - JOUR
T1 - Normal form and global solutions for the Klein-Gordon-Zakharov equations
AU - Ozawa, T.
AU - Tsutaya, K.
AU - Tsutsumi, Y.
N1 - Publisher Copyright:
© 2016 L'Association Publications de l'Institut Henri Poincaré
PY - 1995/7/1
Y1 - 1995/7/1
N2 - In this paper we study the global existence and asymptotic behavior of solutions for the Cauchy problem of the Klein-Gordon-Zakharov equations in three space dimensions. We prove that for small initial data, there exist the unique global solutions of the Klein-Gordon-Zakharov equations. We also show that these solutions approach asymptotically the free solutions as t → ∞. Our proof is based on the method of normal forms introduced by Shatah [12], which transforms the original system with quadratic nonlinearity into a new system with cubic nonlinearity.
AB - In this paper we study the global existence and asymptotic behavior of solutions for the Cauchy problem of the Klein-Gordon-Zakharov equations in three space dimensions. We prove that for small initial data, there exist the unique global solutions of the Klein-Gordon-Zakharov equations. We also show that these solutions approach asymptotically the free solutions as t → ∞. Our proof is based on the method of normal forms introduced by Shatah [12], which transforms the original system with quadratic nonlinearity into a new system with cubic nonlinearity.
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U2 - 10.1016/S0294-1449(16)30156-1
DO - 10.1016/S0294-1449(16)30156-1
M3 - Article
AN - SCOPUS:85011632558
SN - 0294-1449
VL - 12
SP - 459
EP - 503
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -