Scattering for a defocusing inhomogeneous Hartree equation in the mass-subcritical regime
Abstract
We investigate the scattering behavior of global energy solutions to the inhomogeneous defocusing generalized Hartree equation $ i\partial_t \varphi+\Delta \varphi = |x|^{-{\varrho}}|\varphi|^{\beta-2}\bigl(J_\gamma *|\cdot|^{-{\varrho}}|\varphi|^{\beta}\bigr)\varphi, \qquad {\varrho}>0,\ \beta>2. $ This work complements our earlier study (Acta Appl. Math., 177, no. 6 (2022)) on the radial case by removing the spherical symmetry assumption under the additional condition $ x\varphi_0\in L^2 $. The novelty is to establish the scattering in weighted Sobolev spaces within the mass-subcritical range$ \beta_0
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Evolution equations and control theory
- Volume
- 20
- Issue
- 0
- Pages
- 122–147
- Publication date
- 1 January 2026