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Persistence of conormal analyticity for the Euler equations in the half-space
Abstract
We prove the persistence of conormal analyticity through the Hr norm, with r ≥ 4, for the 3D incompressible Euler equations in the half-space Ω= ℝ+3. We also establish a lower bound on the radius of conormal analyticity which depends on |u|Hr and initial data. In particular, persistence is established in both of the spaces Xτco and Aτco, the former being based on the conormal operator Zk = ϕk ∂3k and the latter being based on Lk = (ϕ∂3)k. Finally, we show that the norms |· |Xτco and |· |Aτco are equivalent up to a small loss in radius, the proof of which uses explicit identities relating the two conormal operators.
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BibTeX
@misc{ingimarson2026persistence,
title = {{Persistence of conormal analyticity for the Euler equations in the half-space}},
author = {Benjamin Ingimarson and Igor Kukavica and Marco Sammartino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14408},
eprint = {2610.14408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14408},
}
RIS
TY - UNPB
TI - Persistence of conormal analyticity for the Euler equations in the half-space
AU - Benjamin Ingimarson
AU - Igor Kukavica
AU - Marco Sammartino
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14408
UR - https://arxiv.org/abs/2610.14408
AB - We prove the persistence of conormal analyticity through the H^r norm, with r ≥ 4, for the 3D incompressible Euler equations in the half-space Ω= ℝ_+^3. We also establish a lower bound on the radius of conormal analyticity which depends on |u|_H^r and initial data. In particular, persistence is established in both of the spaces X_τ^co and A_τ^co, the former being based on the conormal operator Z_k = ϕ^k ∂_3^k and the latter being based on L^k = (ϕ∂_3)^k. Finally, we show that the norms |· |_X_τ^co and |· |_A_τ^co are equivalent up to a small loss in radius, the proof of which uses explicit identities relating the two conormal operators.
ER -