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arXiv · 1907.06964

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

D. Mukherjee·P. T. Nam·P. T. Nguyen
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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.

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D. Mukherjee, P. T. Nam, P. T. Nguyen. 2019-07-16. Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential. https://arxiv.org/abs/1907.06964

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