Publication details

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


MUKHERJEE Debangana NAM Phan Thanh NGUYEN Phuoc Tai

Year of publication 2021
Type Article in Periodical
Magazine / Source Journal of Functional Analysis
MU Faculty or unit

Faculty of Science

Keywords Nonlinear Schrodinger equation; Inverse square potential; Hardy-Gagliardo-Nirenberg inequality; Ground state solutions
Description We consider the focusing nonlinear Schrodinger 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.
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