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