Remarks on global existence for the supercritical nonlinear Schrödinger equation with a harmonic potential |
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Authors: | Guanggan Chen Jian Zhang |
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Institution: | College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China |
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Abstract: | This paper is concerned with the nonlinear Schrödinger equation with a harmonic potential which describes the attractive Bose–Einstein condensate under the magnetic trap. By combining the best constant of Gagliardo–Nirenberg's inequality with the characteristic of this equation, we derive out a global existence condition for the supercritical equation which coincides with the critical case. |
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Keywords: | Global existence Supercritical Nonlinear Schrö dinger equation Harmonic potential |
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