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Global well-posedness and scattering results for Dirac Hartree-type equations with small initial data. (arXiv:1710.11524v2 [math.AP] UPDATED)
来源于:arXiv
We consider the Dirac equation with cubic Hartree-tpye nonlinearity derived
by uncoupling the Maxwell-Dirac or Dirac-Klein-Gordon systems. We prove small
data scattering result. Main ingredients of the proof are the localized
strichartz estimates and improved bilnear estimates thanks to null-structure
hidden in Dirac operator. We apply the projection operator and get system of
equations which we work on. This result is shown to be optimal by proving
iteration method based on Duhamel's formula of the system over superciritical
range fails. 查看全文>>