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Center-stable manifold of the ground state in the energy space for the critical wave equation

Krieger, Joachim ; Nakanishi, Kenji ; Schlag, Wilhelm

In: Mathematische Annalen, 2015, vol. 361, no. 1-2, p. 1-50

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    Titre
    • Center-stable manifold of the ground state in the energy space for the critical wave equation
    Auteur
    • Krieger, Joachim. Bâtiment des Mathématiques, EPFL, Station 8, 1015, Lausanne, Switzerland
    • Nakanishi, Kenji. Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan
    • Schlag, Wilhelm. Department of Mathematics, The University of Chicago, 5734 South University Avenue, 60615, Chicago, IL, USA
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Mathematische Annalen, 2015, vol. 361, no. 1-2, p. 1-50. Springer Berlin Heidelberg
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:332389
    Summary
    We construct a center-stable manifold of the ground state solitons in the energy space for the critical wave equation without imposing any symmetry, as the dynamical threshold between scattering and blow-up, and also as a collection of solutions which stay close to the ground states. Up to energy slightly above the ground state, this completes the 9-set classification of the global dynamics in our previous paper (DCDS 33:6, 2013). We can also extend the manifold to arbitrary energy size by adding large radiation. The manifold contains all the solutions scattering to the ground state solitons, and also some of those blowing up in finite time by concentration of the ground states.