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
Stable Self-Similar Blow-Up Dynamics for Slightly {L^2}-Supercritical Generalized KDV Equations
TL;DR: In this paper, the existence and stability of a blow-up dynamics with self-similar blowup rate in the energy space was proved and a specific description of the formation of the singularity near the blowup time was given.
Posted Content
Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
Michael Ruzhansky,Michael Ruzhansky,Niyaz Tokmagambetov,Niyaz Tokmagambetov,Nurgissa Yessirkegenov,Nurgissa Yessirkegenov +5 more
TL;DR: In this article, the dependence of the best constants in Sobolev and Gagliardo-Nirenberg inequalities on the precise form of the Soboleve space norm is investigated.
Journal ArticleDOI
Near soliton dynamics and singularity formation for L^2 critical problems
Yvan Martel,Frank Merle,Frank Merle,Pierre Raphaël,Pierre Raphaël,Jeremie Szeftel,Jeremie Szeftel +6 more
TL;DR: In this paper, a survey of the state of the art concerning singularity formation for two canonical dispersive problems: the critical non-linear Schrodinger equation and the critical generalized KdV equation is presented.
Journal ArticleDOI
Control of rare intense events in spatiotemporally chaotic systems.
Viktor Nagy,Edward Ott +1 more
TL;DR: This work addresses the problem of using feedback control for the purpose of suppressing rare intense events in spatially extended systems and investigates the use of control to suppress turbulent spikes in the complex Ginzburg-Landau equation in the limit of small dissipation.
Journal ArticleDOI
Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II
TL;DR: In this paper, the Cauchy problem for higher-order degenerate quasilinear partial differential equations (PDEs) was studied analytically and numerically.
References
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