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


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 \({N \geqslant 1}\).


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

Mathematics Subject Classification

35Q55 35B44 35C06 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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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