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Abstract We consider the 1-equivariant energy critical wave maps problem with two-sphere target. Using a method based on matched asymptotic expansions, we construct infinite time relaxation, blow-up, and intermediate types of solutions that have topological degree one. More precisely, for a symbol class of admissible, time-dependent length scales, we construct solutions which can be decomposed as a ground state harmonic map (soliton) re-scaled by an admissible length scale, plus radiation, and small corrections which vanish (in a suitable sense) as time approaches infinity. Our class of admissible length scales includes positive and negative powers of t, with exponents sufficiently small in absolute value. In addition, we obtain solutions with soliton length scale undergoing damped or undamped oscillations in a bounded set, or undergoing unbounded oscillations, for all sufficiently large t.
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This content will become publicly available on May 27, 2026
Brill waves with slow fall-off towards spatial infinity
Abstract We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some representative solutions. We numerically construct an explicit example with slow-off which does not exhibit antipodal symmetry at spatial infinity.
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- PAR ID:
- 10598306
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Classical and Quantum Gravity
- Volume:
- 42
- Issue:
- 11
- ISSN:
- 0264-9381
- Page Range / eLocation ID:
- 115011
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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