数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1835-1850.doi: 10.1016/S0252-9602(12)60144-1

• 论文 • 上一篇    下一篇

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

毋海根1|张军勇2   

  1. 1.School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; 2.Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2011-03-21 修回日期:2011-06-28 出版日期:2012-09-20 发布日期:2012-09-20
  • 基金资助:

    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, and Doctoral Foundation of Henan Polytechnic University.

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

 WU Hai-Gen1, ZHANG Jun-Yong2   

  1. 1.School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; 2.Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2011-03-21 Revised:2011-06-28 Online:2012-09-20 Published:2012-09-20
  • Supported by:

    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, and 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.

关键词: Klein-Gordon equation, Hartree nonlinearity, decay estimate, scattering the-ory

Abstract:

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.

Key words: Klein-Gordon equation, Hartree nonlinearity, decay estimate, scattering the-ory

中图分类号: 

  • 35P25