Communications in Mathematical Sciences

Volume 14 (2016)

Number 4

Globally smooth solution and blow-up phenomenon for a nonlinearly coupled Schrödinger system in atomic Bose–Einstein condensates

Pages: 1005 – 1021

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n4.a7

Authors

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Qiaoxin Li (Graduate School of the China Academy of Engineering Physics, Beijing, China)

Xinglong Wu (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China)

Abstract

In this paper, we study the nonlinearly coupled Schrödinger equations for atomic Bose–Einstein condensates. By the Galërkin method and a priori estimates, the global existence of a smooth solution is obtained. Under some assumptions of the coefficients and $p$, the blow-up theorem is established.

Keywords

Galërkin method, locally smooth solution, globally smooth solution, <i>a priori</i> estimates, blow-up solution

2010 Mathematics Subject Classification

35E15, 35Q53

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Published 6 April 2016