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Soliton resolution for energy-critical wave maps in the equivariant case

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arxiv 2106.10738 v2 pith:QJN5KCS2 submitted 2021-06-20 math.AP

Jacek Jendrej , Andrew Lawrie This is my paper · ORCID
classification math.AP
keywords mapsmathbbequivariantwaveasymptoticallycaseclassesconsider
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abstract

We consider the equivariant wave maps equation $\mathbb{R}^{1+2} \to \mathbb{S}^2$, in all equivariance classes $k \in \mathbb{N}$. We prove that every finite energy solution resolves, continuously in time, into a superposition of asymptotically decoupling harmonic maps and free radiation.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classification of kink clusters for scalar fields in dimension 1+1

    math.AP 2024-12 accept novelty 8.0 of 10

    For general 1+1 scalar field models, every kink n-cluster obeys a universal asymptotic law with gaps 2 log(κt) - log(Mk(n-k)/2), and all such clusters form an n-dimensional manifold parameterized by kink positions.

  2. Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordstr\"om black hole

    math.AP 2025-01 reject novelty 7.0 of 10

    For the Bizon-Kahl Yang-Mills kink in an extremal Reissner-Nordström background, globally bounded perturbations are shown to converge locally in space, and a finite-codimensional stable manifold is built.

  3. 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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