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Nonlinear Inviscid Damping of Couette Flow with Vorticity Perturbations Supported up to the Boundary
Abstract
We establish nonlinear inviscid damping of the near-Couette flows in a finite channel, with vorticity perturbations vanishing to infinite order at the boundary. To study the boundary effect, we decompose the vorticity into dyadic layers whose supports expand toward the boundary, and use an inductive Newton scheme to track nonlinear interactions across layers. Finally, precise elliptic estimates are established to quantify the velocity generated by different layers.
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BibTeX
@misc{he2026nonlinear,
title = {{Nonlinear Inviscid Damping of Couette Flow with Vorticity Perturbations Supported up to the Boundary}},
author = {Siming He and Sameer Iyer and Weiren Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29975},
eprint = {2610.29975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29975},
}
RIS
TY - UNPB
TI - Nonlinear Inviscid Damping of Couette Flow with Vorticity Perturbations Supported up to the Boundary
AU - Siming He
AU - Sameer Iyer
AU - Weiren Zhao
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29975
UR - https://arxiv.org/abs/2610.29975
AB - We establish nonlinear inviscid damping of the near-Couette flows in a finite channel, with vorticity perturbations vanishing to infinite order at the boundary. To study the boundary effect, we decompose the vorticity into dyadic layers whose supports expand toward the boundary, and use an inductive Newton scheme to track nonlinear interactions across layers. Finally, precise elliptic estimates are established to quantify the velocity generated by different layers.
ER -