PreprintCC BY 4.0arXiv
Sharp Global Well-Posedness for the Logarithmically Regularized 2D Euler Equations
Abstract
We consider solutions to the two-dimensional Euler equations with a logarithmically regularized velocity given by u=∇⊥(−Δ)−1ln−γ(|∇|+e)ω and initial vorticity in Ḣ1 ∩ Ḣ−1(ℝ2). We show that if γ>1/2, then global well-posedness holds.
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BibTeX
@misc{radke2026sharp,
title = {{Sharp Global Well-Posedness for the Logarithmically Regularized 2D Euler Equations}},
author = {Zachary Radke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18775},
eprint = {2610.18775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp Global Well-Posedness for the Logarithmically Regularized 2D Euler Equations
AU - Zachary Radke
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.18775
UR - https://arxiv.org/abs/2610.18775
AB - We consider solutions to the two-dimensional Euler equations with a logarithmically regularized velocity given by u=∇^⊥(−Δ)^−1ln^−γ(|∇|+e)ω and initial vorticity in Ḣ^1 ∩ Ḣ^−1(ℝ^2). We show that if γ>1/2, then global well-posedness holds.
ER -