The focusing cubic NLS with inverse-square potential in three space dimensions

Abstract

We consider the focusing cubic nonlinear Schrödinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS. We also prove failure of uniform space-time bounds at the threshold.

35 pages

References in corpus (5)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Quintic NLS in the exterior of a strictly convex obstacle
• The energy-critical NLS with inverse-square potential
• Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ${\mathbb{R}}^3$
• The focusing cubic NLS on exterior domains in three dimensions

Cited by in corpus (7)

• Focusing NLS with inverse square potential
• On stability and instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential
• Minimal mass blow-up solutions for the $L^2$ critical 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 radial focusing INLS equation in higher dimensions
• Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential
• Global Dynamics below the standing waves for the focusing semilinear Schrödinger equation with a repulsive Dirac delta potential