Work

Nonlinear Inviscid Damping of Couette Flow with Vorticity Perturbations Supported up to the Boundary

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29975

Authors: He, Siming, Iyer, Sameer, Zhao, Weiren

Institutions: University of South Carolina, University of California, Davis, New York University Abu Dhabi

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W7223225747

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