GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION  

作　　者：霍朝辉 

机构地区：[1]Institute of Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Acta Mathematica Scientia》2016年第4期1117-1152,共36页数学物理学报（B辑英文版）

基　　金：supported by the NSF of China(11471323)

摘　　要：The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space is considered. It is shown that it is globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 if small initial data （u0 （x）, u1 （x）, n0 （x）, n1 （x）） ∈ （H^1 ×L^2× L^2 × H^-1）. It answers an open problem： Is it globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 for 3D Klein-Gordon- Zakharov equation with small initial data [1, 2]？ The method in this article combines the linear property of the equation （ dispersive property） with nonlinear property of the equation （energy inequalities）. We mainly extend the spaces F^s and N^3 in one dimension [3] to higher dimension.The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space is considered. It is shown that it is globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 if small initial data （u0 （x）, u1 （x）, n0 （x）, n1 （x）） ∈ （H^1 ×L^2× L^2 × H^-1）. It answers an open problem： Is it globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 for 3D Klein-Gordon- Zakharov equation with small initial data [1, 2]？ The method in this article combines the linear property of the equation （ dispersive property） with nonlinear property of the equation （energy inequalities）. We mainly extend the spaces F^s and N^3 in one dimension [3] to higher dimension.

关 键 词：Global well-posedness 3D Klein-Gordon-Zakharov equation dyadic Xs b spacesin higher dimension 

分 类 号：O175[理学—数学]