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2002 Lower bounds for the $L^2$ minimal periodic blow-up solutions of critical nonlinear Schrödinger equation
Christophe Antonini
Differential Integral Equations 15(6): 749-768 (2002).

Abstract

We consider the nonlinear Schrödinger equation with critical power $iu_t=-\Delta u-|u|^{4/N}u$, $t\geq 0$ and $x\in\mathbb T^N$ (the space-periodic case) in $H^1$. We consider a blow-up solution with minimal mass. We obtain in this context an optimal lower bound for the blow-up rate (that is, for $ | {\nabla u(t)}| _{L^2}$), and we observe that this lower bound equals the blow-up rate (which is explicitly known) of the minimal blow-up solutions in $\mathbb R^N$.

Citation

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Christophe Antonini. "Lower bounds for the $L^2$ minimal periodic blow-up solutions of critical nonlinear Schrödinger equation." Differential Integral Equations 15 (6) 749 - 768, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1016.35018
MathSciNet: MR1893845

Subjects:
Primary: 35Q55
Secondary: 35B10 , 35B45 , 35Q40

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 6 • 2002
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