Scattering theory for Hartree equations with inverse-square potentials

Abstract

Scattering theory for Hartree equations with inverse-square potentials (HE) are considered. Recently, Suzuki [1, 2] studied the global solvability and blowup in finite time for (HE). To observe more precise properties for global solutions, it is suitable to consider the asymptotic behavior, especially, scattering problem.

Keywords:

• Hartree equations
• nonlinear Schrödinger equation
• Hardy inequality
• scattering theory
• wave operator
• virial identity
• inverse-square potentials

AMS Subject Classifications:

• Primary: 35Q55
• 35Q40
• Secondary: 81Q15

Acknowledgements

The author would like to thank the referees for reading the manuscript carefully.

Notes

No potential conflict of interest was reported by the author.