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.

arXiv commentTypos corrected

References in corpus (4)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Scattering theory in a weighted $L^2$ space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Scattering for the radial focusing INLS equation in higher dimensions

Cited by in corpus (14)

• On the inhomogeneous NLS with inverse-square potential
• On well-posedness and concentration of blow-up solutions for the intercritical inhomogeneous NLS equation
• A remark on the scattering theory for the 2d radial focusing INLS
• Scattering of radial data in the focusing NLS and generalized Hartree equations
• On the GWP of focusing energy-ciritical inhomogeneous NLS
• Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation
• Long time dynamics and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with spatial growing nonlinearity
• NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
• Long time behaviors for the inhomogeneous NLS with a potential in ${\mathbb{R}}^3$
• The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential
• The Cauchy problem for the critical inhomogeneous nonlinear Schrödinger equation in $H^s({\mathbb{R}}^n)$
• Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in $H^s({\mathbb{R}}^n)$
• Interpolation scattering for wave equations with singular potentials and singular data
• Scattering theory for 3d cubic inhomogeneous NLS with inverse square potential