Abstract
This paper studies the dynamical properties of blow-up solutions for nonlinear Schrödinger equation with partial confinement, which may model the Bose-Einstein condensate under a partial trap potential. By using the variational characteristic of the classic nonlinear scalar field equation and the Hamilton conservations, we first get the threshold for global existence and blow-up of the Cauchy problem on mass in two-dimensional space. Then, in terms of the refined compactness Lemma and the variational characteristic of the ground state of nonlinear scalar field equation, we get mass concentration properties of the blow-up solutions as well as limiting profile of the blow-up solutions with small super-critical mass.
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