Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential

2019/07/16 by Debashis Mukherjee, Phan Thành Nam, Mukherjee, D. +3 · 2 citations
Mathematics · Physics and Astronomy · Engineering · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1907.06964

Abstract

We consider the focusing nonlinear Schrödinger equation with the critical inverse square potential. We give the first proof of the uniqueness of the ground state solution. Consequently, we obtain a sharp Hardy-Gagliardo-Nirenberg interpolation inequality. Moreover, we provide a complete characterization for the minimal mass blow-up solutions to the time dependent problem.

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• Nonlinear Schr�dinger equations and sharp interpolation estimates
• Existence of solitary waves in higher dimensions

Cited by

• Nonlinear scalar field equations with a critical Hardy potential
• Optimizers of the Finite-Rank Hardy-Lieb-Thirring Inequality for Hardy-Schrödinger Operator

Related

• L² concentration of blow-up solutions for the mass-critical NLS with inverse-square potential
• Ground state of the mass-critical inhomogeneous nonlinear Schrodinger functional
• Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schrödinger Equation
• Minimal mass blow up solutions for a double power nonlinear Schrödinger equation
• Ground state energy threshold and blow-up for NLS with competing nonlinearities