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GLOBAL SOLUTIONS OF SEMIRELATIVISTIC HARTREE TYPE EQUATIONS

  • Cho, Yong-Geun (Department of Mathematics Pohang University of Science and Technology) ;
  • Ozawa, Tohru (Department of Mathematics Hokkaido University)
  • Published : 2007.09.30

Abstract

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.

Keywords

semirelativistic Hartree type equations;global existence;scattering;Coulomb type potentials

References

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Cited by

  1. Small data scattering for semi-relativistic equations with Hartree type nonlinearity vol.259, pp.10, 2015, https://doi.org/10.1016/j.jde.2015.06.037
  2. The Boson star equation with initial data of low regularity vol.97, 2014, https://doi.org/10.1016/j.na.2013.11.023
  3. Modified Scattering for the Boson Star Equation vol.332, pp.3, 2014, https://doi.org/10.1007/s00220-014-2094-x