Focusing NLS with inverse square potential

Abstract

In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schrödinger equation with inverse square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space $H_a^1({\mathbb{R}}^d)$ in dimensions $d\ge 3$, which extends the result of [10,11] to higher dimensions cases but with radial initial data. The new ingredient is to establish the dispersive estimate for radial function and overcome the weak dispersive estimate when $a<0$.

arXiv comment15 pages, comments are welcome

References in corpus (4)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• The fundamental solution and Strichartz estimates for the Schrödinger equation on flat euclidean cones
• The focusing cubic NLS with inverse-square potential in three space dimensions
• Global-in-time Strichartz estimates and cubic Schrödinger equation in a conical singular space

Cited by in corpus (7)

• On the inhomogeneous NLS with inverse-square potential
• The $W^{s,p}$-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential
• Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation
• Global dynamics below the ground state for the focusing Schrödinger equation with a potential
• Scattering theory for 3d cubic inhomogeneous NLS with inverse square potential
• Long time behaviors for the inhomogeneous NLS with a potential in ${\mathbb{R}}^3$
• Focusing nonlinear Hartree equation with inverse-square potential