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Soliton resolution for critical co-rotational wave maps and radial cubic wave equation

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arxiv 2103.01293 v1 pith:CEJKN7HZ submitted 2021-03-01 math.AP

Thomas Duyckaerts , Carlos Kenig , Yvan Martel , Frank Merle This is my paper · ORCID
classification math.AP
keywords equationwaveenergyspaceco-rotationalcubicproveradial
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In this paper we prove the soliton resolution conjecture for all times, for all solutions in the energy space, of the co-rotational wave map equation. To our knowledge this is the first such result for all initial data in the energy space for a wave-type equation. We also prove the corresponding results for radial solutions, which remain bounded in the energy norm, of the cubic (energy-critical) nonlinear wave equation in space dimension 4.

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  1. The large time asymptotics of nonlinear multichannel Schroedinger equations

    math.AP 2025-01 conditional novelty 7.0 of 10

    Radial solutions with bounded H^1 norm decompose asymptotically into a free wave and a weakly localized component, for a broad class of nonlinear and time-dependent interactions.

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