Scattering of radial solutions to the Inhomogeneous Nonlinear Schr\"odinger Equation

Abstract

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation \begin{equation} iu_t + \Delta u + |x|^{-b}|u|^{p-1}u=0, \end{equation} when $b \geq 0$ and $N > 2$ in the intercritical case $0 < s_c <1$. This work generalizes the results of Farah and Guzm\'an [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 Schr\"odinger equation ($b = 0$), extending the work in [6] for radial solutions in all intercritical cases.