Stability of standing waves for the L²-critical Hartree equations with harmonic potential

Juan Huang Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China; College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, ChinaCorrespondence[email protected]

Jian Zhang Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China; College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Xiaoguang Li Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China; College of Economics and Management Science, Sichuan Normal University, Chengdu 610066, China

Abstract

This article is concerned with the Hartree equations with harmonic potential. By an elaborate mathematical analysis, we obtain a sharp stability threshold of this equation. Then with this threshold, we prove that the standing wave of this equation exists and is stable.

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Acknowledgements

This project is supported by the National Science Foundation of China (Grant Nos. 10771151, 10901115 and 11126335), the Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 10ZB003), and the Scientific Research Fund of Sichuan Provincial Science, Technology Department (Grant No. 2010JY0057) and Sichuan Province Science Foundation for Youths (Grant No. 2012JQ0011).

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Stability of standing waves for the L²-critical Hartree equations with harmonic potential

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Stability of standing waves for the L2-critical Hartree equations with harmonic potential

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Stability of standing waves for the L²-critical Hartree equations with harmonic potential