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Global existence of the s-Schrödinger maps in n ≥ 5
Abstract
We study the s-Schrödinger map equation ∂t u = −u ∧ (−Δ)s u on ℝn × ℝ u: ℝn × ℝ → 𝕊2 u(x,0) = u0. For s ∈ (1/2,1) and n ≥ 5 we prove that for small initial data u0 in the critical Besov space one can obtain a global solution.
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BibTeX
@misc{dughayshim2026global,
title = {{Global existence of the $s$-Schrödinger maps in $n \geq 5$}},
author = {Ahmed Dughayshim and Armin Schikorra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17668},
eprint = {2610.17668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17668},
}
RIS
TY - UNPB
TI - Global existence of the s-Schrödinger maps in n ≥ 5
AU - Ahmed Dughayshim
AU - Armin Schikorra
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17668
UR - https://arxiv.org/abs/2610.17668
AB - We study the s-Schrödinger map equation ∂_t u = −u ∧ (−Δ)^s u on ℝ^n × ℝ u: ℝ^n × ℝ → 𝕊^2 u(x,0) = u_0. For s ∈ (1/2,1) and n ≥ 5 we prove that for small initial data u_0 in the critical Besov space one can obtain a global solution.
ER -