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Rigidity results for Euler flows in two dimensional exterior domains
Abstract
We study steady solutions of the two dimensional incompressible Euler equations in the exterior of a compact domain. We assume that fluid enters the exterior domain through every point of the obstacle boundary. Under suitable assumptions on the direction and decay of the velocity at infinity, we prove that the flow is irrotational if and only if the velocity has no stagnation points.
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BibTeX
@misc{alonsooran2026rigidity,
title = {{Rigidity results for Euler flows in two dimensional exterior domains}},
author = {Diego Alonso-Orán and Daniel Sánchez-Simón del Pino and Juan J. L. Velázquez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06309},
eprint = {2610.06309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06309},
}
RIS
TY - UNPB
TI - Rigidity results for Euler flows in two dimensional exterior domains
AU - Diego Alonso-Orán
AU - Daniel Sánchez-Simón del Pino
AU - Juan J. L. Velázquez
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06309
UR - https://arxiv.org/abs/2610.06309
AB - We study steady solutions of the two dimensional incompressible Euler equations in the exterior of a compact domain. We assume that fluid enters the exterior domain through every point of the obstacle boundary. Under suitable assumptions on the direction and decay of the velocity at infinity, we prove that the flow is irrotational if and only if the velocity has no stagnation points.
ER -