Journal of Evolution Equations

, Volume 16, Issue 2, pp 483–500 | Cite as

Classification of minimal mass blow-up solutions for an \({L^{2}}\) critical inhomogeneous NLS

Open Access
Article

Abstract

We establish the classification of minimal mass blow-up solutions of the \({L^{2}}\) critical inhomogeneous nonlinear Schrödinger equation
$$i\partial_t u + \Delta u + |x|^{-b}|u|^{\frac{4-2b}{N}}u = 0,$$
thereby extending the celebrated result of Merle (Duke Math J 69(2):427–454, 1993) from the classic case \({b=0}\) to the case \({0< b< {\rm min} \{2,N\} }\), in any dimension \({N \geqslant 1}\).

Keywords

Inhomogeneous NLS \({L^{2}}\) critical Blow-up Self-similar Critical mass 

Mathematics Subject Classification

35Q55 35B44 35C06 

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Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.UMR 8524 - Laboratoire Paul PainlevéUniversité de Lille, CNRSLilleFrance
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands

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