SCATTERING OF THE FOCUSING ENERGY-CRITICAL NLS WITH INVERSE SQUARE POTENTIAL

Kai Yang; Xiaoyi Zhang

doi:10.3934/dcds.2023022

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SCATTERING OF THE FOCUSING ENERGY-CRITICAL NLS WITH INVERSE SQUARE POTENTIAL

Journal article

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SCATTERING OF THE FOCUSING ENERGY-CRITICAL NLS WITH INVERSE SQUARE POTENTIAL

Kai Yang and Xiaoyi Zhang

Discrete and continuous dynamical systems. Series A, Vol.43(7), pp.2608-2636

03/01/2023

DOI: 10.3934/dcds.2023022

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Abstract

We consider the Cauchy problem for the focusing energy-critical nonlinear Schrodinger equation with an inverse square potential in dimension d = 4, 5, 6. We show that if the supremum of the kinetic energy of a solu-tion over its maximal lifespan is less than the kinetic energy of the ground state, then the solution must exist globally in time and scatter in both time directions. We develop the "long-term kinetic energy decoupling" associated with the appearance of inverse square potential. No radial assumption is made on the initial data. This extends the result in [22] by the first author to the non-radial case.

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Physical Sciences

Mathematics, Applied

Science & Technology

Details

Title: Subtitle: SCATTERING OF THE FOCUSING ENERGY-CRITICAL NLS WITH INVERSE SQUARE POTENTIAL
Creators: Kai Yang - Southeast University
Xiaoyi Zhang - University of Iowa
Resource Type: Journal article
Publication Details: Discrete and continuous dynamical systems. Series A, Vol.43(7), pp.2608-2636
DOI: 10.3934/dcds.2023022
ISSN: 1078-0947
eISSN: 1553-5231
Publisher: Amer Inst Mathematical Sciences-Aims
Number of pages: 29
Grant note: Jiangsu Shuang Chuang Doctoral Plan BK20200346 / NSF of Jiangsu Province (China) Simons Collaboration Grant
Language: English
Electronic publication date: 03/01/2023
Academic Unit: Mathematics
Record Identifier: 9984380463002771

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