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

Jacek Jendrej; Andrew Lawrie

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

Analysis of PDEs 2022-01-24 v2

Authors: Jacek Jendrej , Andrew Lawrie

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.

Keywords

wave maps soliton resolution equivariant case energy-critical harmonic maps

Cite

@article{arxiv.2106.10738,
  title  = {Soliton resolution for energy-critical wave maps in the equivariant case},
  author = {Jacek Jendrej and Andrew Lawrie},
  journal= {arXiv preprint arXiv:2106.10738},
  year   = {2022}
}

Comments

78 pages; in the new version we have included Proposition 1.6 (and its proof in Section 5.4), which shows that the only solutions that are pure multi-bubbles in both time directions are the stationary solutions

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