PreprintCC BY 4.0arXiv
Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity
Abstract
We construct two distinct solutions of the two-dimensional incompressible Euler equation with the same initial vorticity in ⋂1≤ p<∞Lp(ℝ2). The vorticities are compactly supported in space and have mean zero, so the corresponding velocities have finite energy. The nonuniqueness mechanism is a cascade of transitions in quadrupole dynamics across infinitely many scales.
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BibTeX
@misc{choi2026nonuniqueness,
title = {{Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity}},
author = {Hyungjun Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37653},
eprint = {2610.37653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37653},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity
AU - Hyungjun Choi
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37653
UR - https://arxiv.org/abs/2610.37653
AB - We construct two distinct solutions of the two-dimensional incompressible Euler equation with the same initial vorticity in ⋂_1≤ p<∞L^p(ℝ^2). The vorticities are compactly supported in space and have mean zero, so the corresponding velocities have finite energy. The nonuniqueness mechanism is a cascade of transitions in quadrupole dynamics across infinitely many scales.
ER -