PreprintarXiv licencearXiv
Construction of infinite time bubble tower solutions for energy critical equivariant Schrödinger maps
Abstract
We prove the existence of infinite time bubble tower solutions for energy critical k-equivariant Schrödinger maps ℝ2→ 𝕊2 with k≥ 3. More precisely, for any integers k≥ 3 and N≥ 1, we construct a k-equivariant solution that is global in one time direction and decomposes asymptotically into a superposition of N bubbles with scales λj(t)∼|t|−βj, where βj=1/2((k/(k−2))N−j−1). Our approach is a backward construction combined with modulation analysis and high order energy estimates. We use Darboux coordinates adapted to the multi bubble profile to express the remainder in a complex scalar form. A key ingredient is the construction of a correction that cancels the leading effect of the nonlinear defect.
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BibTeX
@misc{yin2026construction,
title = {{Construction of infinite time bubble tower solutions for energy critical equivariant Schrödinger maps}},
author = {Yuchen Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05075},
eprint = {2610.05075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05075},
}
RIS
TY - UNPB
TI - Construction of infinite time bubble tower solutions for energy critical equivariant Schrödinger maps
AU - Yuchen Yin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05075
UR - https://arxiv.org/abs/2610.05075
AB - We prove the existence of infinite time bubble tower solutions for energy critical k-equivariant Schrödinger maps ℝ^2→ 𝕊^2 with k≥ 3. More precisely, for any integers k≥ 3 and N≥ 1, we construct a k-equivariant solution that is global in one time direction and decomposes asymptotically into a superposition of N bubbles with scales λ_j(t)∼|t|^−β_j, where β_j=1/2((k/(k−2))^N−j−1). Our approach is a backward construction combined with modulation analysis and high order energy estimates. We use Darboux coordinates adapted to the multi bubble profile to express the remainder in a complex scalar form. A key ingredient is the construction of a correction that cancels the leading effect of the nonlinear defect.
ER -