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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On mass - critical NLS with local and non-local nonlinearities
Vladimir Georgiev,Yan Li +1 more
TL;DR: In this paper , the existence and non-degeneracy of the ground state of the nonlinear Schrödinger equation with double L-critical nonlinearities were proved.
Peer Review
Recent progress on multi-bubble blow-ups and multi-solitons to (stochastic) focusing nonlinear Schr\"odinger equations
TL;DR: In this article , the authors review the recent progress on the long-time behavior for a general class of focusing $L 2$-critical nonlinear Schrodinger equations (NLS) with lower order perturbations.
Journal ArticleDOI
On the blow-up phenomenon for a generalized Davey-Stewartson system
TL;DR: In this article, the mass concentration of the minimal blow-up solutions of the Cauchy problem as t → T (blow-up time) is discussed in detail in terms of the ground state.
On blow up for a class of radial Hartree type equations
TL;DR: In this article , a class of Hartree type equations is studied and a quantitative blow up rate for their blow up solutions is proved, which is an analogue of the result by Merle and Raphaël on 3D NLS.
References
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Journal ArticleDOI
Nonlinear scalar field equations, I existence of a ground state
TL;DR: In this article, a constrained minimization method was proposed for the case of dimension N = 1 (Necessary and sufficient conditions) for the zero mass case, where N is the number of dimensions in the dimension N.
BookDOI
The nonlinear Schrödinger equation : self-focusing and wave collapse
TL;DR: In this article, the authors present a basic framework to understand structural properties and long-time behavior of standing wave solutions and their relationship to a mean field generation and acoustic wave coupling.
Journal ArticleDOI
On a class of nonlinear Schro¨dinger equations
TL;DR: In this paper, the existence of standing wave solutions of nonlinear Schrodinger equations was studied and sufficient conditions for nontrivial solutionsu ∈W¯¯¯¯1,2(ℝ�姫 n ) were established.
Journal ArticleDOI
Uniqueness of positive solutions of Δu−u+up=0 in Rn
TL;DR: In this article, the uniqueness of the positive, radially symmetric solution to the differential equation Δu−u+up=0 (with p>1) in a bounded or unbounded annular region in Rn for all n ≥ 1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition decaying to zero in the case of an unbounded region, was established.
Journal ArticleDOI
Nonlinear Schrödinger equations and sharp interpolation estimates
TL;DR: In this paper, a sharp sufficient condition for global existence for the nonlinear Schrodinger equation is obtained for the case σ = 2/N. This condition is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of Nirenberg and Gagliardo.
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On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
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