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
Citations
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Journal ArticleDOI
Determination of blowup type in the parabolic–parabolic Keller–Segel system
TL;DR: In this paper, a parabolic-parabolic Keller-Segel system was considered, and it was shown that each blowup is type II in radial case and type I in general case.
Journal ArticleDOI
Some remarks on the nonlinear Schrödinger equation with fractional dissipation
Mohamad Darwich,Luc Molinet +1 more
TL;DR: In this paper, the Cauchy problem for the L2-critical focussing nonlinear Schrodinger equation with a fractional dissipation was considered and the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for ∇u(t)L2 was proved.
Journal ArticleDOI
Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles
Justin Holmer,Chang Liu +1 more
TL;DR: In this article, the 1D nonlinear Schrodinger equation (NLS) with focusing point nonlinearity was considered and self-similar blow-up solutions belonging to the energy space were obtained by using parabolic cylinder functions.
Posted Content
Monotonicity properties of blow-up time for nonlinear Schr\"{o}dinger equation: numerical tests
TL;DR: In this paper, the dependence of the blow-up time on a parameter in the focusing nonlinear Schrodinger equation was investigated, in the $L 2$-critical and supercritical cases.
Posted Content
On the critical norm concentration for the inhomogeneous nonlinear Schr\"odinger equation
Luccas Campos,Mykael Cardoso +1 more
TL;DR: In this article, the authors considered the inhomogeneous nonlinear Schrodiger equation (INLS) in the case of finite-time blow-up solutions and provided an alternative for the classification of minimal mass blowup solutions.
References
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Uniqueness of positive solutions of Δu−u+up=0 in Rn
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Nonlinear Schrödinger equations and sharp interpolation estimates
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