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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Posted Content
Blow-up in higher-order reaction-diffusion and wave equations: how $\sqrt{log log}$ factor occurs
TL;DR: The origin of non self-similar blow-up in higher-order reaction-diffusion (parabolic), wave (hyperbolic) and nonlinear dispersion equations is explained by a combination of various methods.
Posted Content
Self-similar blow-up profiles for slightly supercritical nonlinear Schr\"odinger equations
TL;DR: In this paper, Sulem et al. constructed radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schr\"odinger equation and showed that these profiles bifurcate from the ground state solitary wave.
Journal ArticleDOI
Profiles of blow-up solutions for the Gross-Pitaevskii equation
Shi-hui Zhu,Jian Zhang +1 more
TL;DR: In this paper, the blow-up solutions of the Cauchy problem for Gross-Pitaevskii equation were analyzed in terms of Merle and Raphael's arguments as well as Carles' transformation.
Journal ArticleDOI
On Uniqueness of Multi-bubble Blow-Up Solutions and Multi-solitons to $$L^2$$-Critical Nonlinear Schrödinger Equations
TL;DR: In this article , the uniqueness of nonlinear Schrödinger equations in the pseudo-conformal space was proved for a large energy class of multi-bubble blow-up solutions.
Dissertation
Sur l’explosion critique et surcritique pour les équations des ondes et de la chaleur semi-linéaires
TL;DR: In this article, a troisieme porte sur la classification des dynamiques possibles pres de l’etat stationnaire radial for l'equation de la chaleur dans le regime dit energie critique, trois scenarios ayant lieu : the stabilisation, l'instabilite par explosion auto-similaire a profil explosif constant en espace, and l'inabilitate par dissipation vers la solution nulle.
References
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On a class of nonlinear Schro¨dinger equations
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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
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