On the decay and scattering for the klein-gordon-hartree equation with radial data |
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| Authors: | Wu Haigen Zhang Junyong |
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| Institution: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China;3. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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| 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. |
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| Keywords: | Klein-Gordon equation Hartree nonlinearity decay estimate scattering theory |
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