ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA  

作　　者：毋海根 张军勇 

机构地区：[1]School of Mathematics and Information Science,Henan Polytechnic University [2]Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences [3]Zhang Junyong Department of Mathematics,Beijing Institute of Technology

出　　处：《Acta Mathematica Scientia》2012年第5期1835-1850,共16页数学物理学报（B辑英文版）

基　　金：H.G.Wu was supported by the National Science Foundation of China (11071057,10801015);China Postdoctoral Science Foundation (20100470570);the Guozhi Xu Posdoctoral Research Foundation;Doctoral Foundation of Henan Polytechnic University

摘　　要：In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0〈γ≤4 and γ〈d with Hartree potential V（x） =｜x｜-γ.In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0〈γ≤4 and γ〈d with Hartree potential V（x） =｜x｜-γ.

关 键 词：Klein-Gordon equation Hartree nonlinearity decay estimate scattering theory 

分 类 号：O175[理学—数学]