Sharp Scattering Threshold for Mass-Subcritical Inhomogeneous NLS and Hartree Equations
A determination of the exact borderline, in terms of the source-term exponent, that separates scattering from non-scattering behavior for mass-subcritical inhomogeneous nonlinear Schrodinger and generalized Hartree equations in the L^2 setting. It proves non-scattering for low exponents and L^2 scattering of global solutions above the threshold, extending dispersive-PDE scattering theory to nonlinearities with a singular spatial weight.
2501.00041
This math.AP paper studies the long-time behavior of some inhomogeneous nonlinear Schrodinger equations (INLS) and a closely related inhomogeneous generalized Hartree equation (INLH), whose nonlinear…