On global solution to the Klein-Gordon-Hartree equation below energy space
نویسندگان
چکیده
In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in R. Making use of Bourgain’s method in conjunction with precise Strichartz estimates of S.Klainerman and D.Tataru, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation, inspired by I. Gallagher and F. Planchon [3]. In doing so a number of nonlinear a prior estimates and using flexibility of Klein-Gordon admissible pairs which are a bit different from wave’s, we define a mixed time-space by using Besov spaces. As we know, we haven’t found any result on low regularity for the Klein-Gordon-Hartree equation.
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