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Remarks on the blow-up rate for critical nonlinear Schrödinger equation with harmonic potential. (English) Zbl 1166.35377
Summary: We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a harmonic potential, which models the attractive Bose-Einstein condensate. We establish the sharp lower and upper bounds of blow-up rate as $t\rightarrow T$ (blow-up time), which improve the result of {\it Q. Liu, Y. Zhou} and {\it J. Zhang} [Appl. Math. Comput. 172, No. 2, 1121--1132 (2006; Zbl 1091.35092)].

35Q55NLS-like (nonlinear Schrödinger) equations
35B40Asymptotic behavior of solutions of PDE
35B45A priori estimates for solutions of PDE
81V80Applications of quantum theory to quantum optics
Full Text: DOI
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