On global solution to the Klein–Gordon–Hartree equation below energy space
- Miao, Changxing
- Zhang, Junyong
DOIAbstract
AbstractIn this paper, we consider the Cauchy problem for Klein–Gordon equation with a cubic convolution nonlinearity in R3. By making use of Bourgain's method in conjunction with a precise Strichartz estimate of S. Klainerman and D. Tataru, we establish the Hs (s<1) global well-posedness of the Cauchy problem for the cubic convolution defocusing Klein–Gordon–Hartree equation. Before arriving at the previously discussed conclusion, we obtain global solution for this non-scaling equation with small initial data in Hs0×Hs0−1 where s0=γ6 but not γ2−1, for this equation that we consider is a subconformal equation in some sense. In doing so a number of nonlinear prior estimates are already established by using Bony's decomposition, flexibility o...
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