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Profiles of bounded radial solutions of the focusing, energy-critical wave equation

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Abstract

In this paper we consider global and non-global bounded radial solutions of the focusing energy-critical wave equation in space dimension 3. We show that any of these solutions decouples, along a sequence of times that goes to the maximal time of existence, as a sum of modulated stationary solutions, a free radiation term and a term going to 0 in the energy space. In the case where there is only one stationary profile, we show that this expansion holds asymptotically without restriction to a subsequence.

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Authors and Affiliations

  1. LAGA, Université Paris 13 (UMR 7539), Villetaneuse, France

    Thomas Duyckaerts

  2. University of Chicago, Chicago, IL, USA

    Carlos Kenig

  3. Cergy-Pontoise (UMR 8088), IHES, Cergy-Pontoise, France

    Frank Merle

Authors
  1. Thomas Duyckaerts
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  2. Carlos Kenig
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  3. Frank Merle
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Corresponding author

Correspondence to Thomas Duyckaerts.

Additional information

T. Duyckaerts was partially supported by ERC Grant Dispeq. C. Kenig was partially supported by NSF Grant DMS-0968472.

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Duyckaerts, T., Kenig, C. & Merle, F. Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Geom. Funct. Anal. 22, 639–698 (2012). https://doi.org/10.1007/s00039-012-0174-7

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  • DOI: https://doi.org/10.1007/s00039-012-0174-7

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