JournalsaihpcVol. 26, No. 4pp. 1361–1386

On asymptotic stability in energy space of ground states of NLS in 2D

  • Scipio Cuccagna

    DISMI, University of Modena and Reggio Emilia, Padiglione Morselli, Reggio Emilia, 42100, Italy

  • Mirko Tarulli

    Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, Pisa, 56127, Italy
On asymptotic stability in energy space of ground states of NLS in 2D cover
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Abstract

We transpose work by K. Yajima and by T. Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schrödinger equation (NLS) in 2D. As an application we extend to dimension 2D a result on asymptotic stability of ground states of NLS proved in the literature for all dimensions different from 2.

Résumé

On utilise les travaux de K. Yajima et T. Mizumachi pour prouver des estimations dispersives et régularisantes des solutions de l'équation linéarisée aux états fondamentaux de NLS in 2D. On applique ces résultats pour obtenir des extensions en dimension 2D de la stabilité asymptotique prouvée en littérature pour toutes les dimensions différentes de 2.

Cite this article

Scipio Cuccagna, Mirko Tarulli, On asymptotic stability in energy space of ground states of NLS in 2D. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, pp. 1361–1386

DOI 10.1016/J.ANIHPC.2008.12.001