Journal ArticleDOI
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation
TLDR
In this paper, the authors consider finite time blow up solutions to the critical nonlinear Schrodinger equation, and prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part correspond to the regular part and has a strong L2 limit at blow up time.Abstract:
We consider finite time blow up solutions to the critical nonlinear Schrodinger equation Open image in new window For a suitable class of initial data in the energy space H1, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part corresponds to the regular part and has a strong L2 limit at blow up time.read more
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Blow up dynamics for smooth equivariant solutions to the energy critical Schr\"odinger map
TL;DR: In this paper, the authors considered the energy critical Schrodinger map problem with the 2-sphere target for equivariant initial data of homotopy index $k = 1.
Journal ArticleDOI
Continuations of the nonlinear Schr\"odinger equation beyond the singularity
G. Fibich,M. Klein +1 more
TL;DR: In this paper, the authors present four continuations of the critical nonlinear \schro equation (NLS) beyond the singularity: a sub-threshold power continuation, a shrinking-hole continuation for ring-type solutions, a vanishing nonlinear-damping continuation, and a complex Ginzburg-Landau (CGL) continuation.
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Blow-up solutions on a sphere for the 3d quintic NLS in the energy space
Justin Holmer,Svetlana Roudenko +1 more
TL;DR: In this article, it was shown that a log-log blow-up solution of the type studied by Merle-Rapha\"el-Szeftel (2001-2005) to the L 2 critical focusing NLS equation can be obtained in the radial energy space.
Journal ArticleDOI
On Singularity formation for the L^2-critical Boson star equation
Enno Lenzmann,Mathieu Lewin +1 more
TL;DR: In this paper, a general, nonperturbative result about finite-time blowup solutions for the $L 2 -critical boson star equation was proved, and it was shown that the limiting measure exhibits minimal mass concentration.
Journal ArticleDOI
Remarks on the Blow-Up Solutions for the Critical Gross-Pitaevskii Equation
Xiaoguang Li,Chong Lai +1 more
TL;DR: In this article, the existence and qualitative properties of the minimal blow-up solutions of the critical Gross-Pitaevskii equation were investigated, where the authors considered the Bose-Einstein condensate.
References
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