Classification of minimal mass blow-up solutions for an $${L^{2}}$$ critical inhomogeneous NLS期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Vianney Combet François Genoud

Institution:	1.UMR 8524 - Laboratoire Paul Painlevé,Université de Lille, CNRS,Lille,France;2.Delft Institute of Applied Mathematics,Delft University of Technology,Delft,The Netherlands

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 ${N \geqslant 1}$.

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