TY - JOUR
T1 - On the decay and scattering for the Klein-Gordon-Hartree equation with radial data
AU - Haigen, Wu
AU - Junyong, Zhang
PY - 2012/9
Y1 - 2012/9
N2 - 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.
AB - 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.
KW - Decay estimate
KW - Hartree nonlinearity
KW - Klein-Gordon equation
KW - Scattering theory
UR - https://www.scopus.com/pages/publications/84865484736
U2 - 10.1016/S0252-9602(12)60144-1
DO - 10.1016/S0252-9602(12)60144-1
M3 - Article
AN - SCOPUS:84865484736
SN - 0252-9602
VL - 32
SP - 1835
EP - 1850
JO - Acta Mathematica Scientia
JF - Acta Mathematica Scientia
IS - 5
ER -