PreprintCC BY 4.0arXiv
Finite-time blowup of the Euler equation without forcing
Abstract
These notes present the construction in \cite{euler} of finite-time blowup for the three-dimensional incompressible, unforced Euler equations on ℝ3: ∂tu+(u·∇)u+∇ p=0, ∇· u=0. The construction successively adds oscillatory layers to smooth parent solutions. Each layer is constructed by a finite expansion and an exact correction, so that the resulting child solves Euler.
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BibTeX
@misc{zheng2026finitetime,
title = {{Finite-time blowup of the Euler equation without forcing}},
author = {Fan Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02509},
eprint = {2610.02509},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02509},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-time blowup of the Euler equation without forcing
AU - Fan Zheng
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02509
UR - https://arxiv.org/abs/2610.02509
AB - These notes present the construction in \cite{euler} of finite-time blowup for the three-dimensional incompressible, unforced Euler equations on ℝ^3: ∂_tu+(u·∇)u+∇ p=0, ∇· u=0. The construction successively adds oscillatory layers to smooth parent solutions. Each layer is constructed by a finite expansion and an exact correction, so that the resulting child solves Euler.
ER -