Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation

Abstract

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schrödinger equation \begin{equation} iu_t + Δu + |x|^{-b}|u|^{p-1}u=0, \end{equation} when $b\ge 0$ and $N>2$ in the intercritical case $0<s_c<1$. This work generalizes the results of Farah and Guzmán [9], allowing a broader range of values for the parameters $p$ and $b$. We use a modified version of Dodson-Murphy's approach [6], allowing us to deal with the inhomogeneity. The proof is also valid for the classical nonlinear Schrödinger equation ($b=0$), extending the work in [6] for radial solutions in all intercritical cases.

Typos corrected