Inviscid damping without derivatives near Couette flow
Abstract
We study the long-time dynamics near Couette flow for the 2D Euler equations in unbounded geometries. We identify a mechanism of nonlinear inviscid damping at Yudovich regularity, distinct from classical phase mixing: velocity decay driven by spatial evacuation of vorticity. The mechanism leads to a geometry-sign classification of the dynamics. In the infinite channel, small nonnegative bounded-vorticity perturbations undergo global damping without derivative assumptions. In the whole plane, small nonnegative perturbations exhibit enhanced dispersion and velocity damping, while non-positive perturbations remain confined and do not damp, even when arbitrarily small in Gevrey classes. Moreover, damping can coexist with infinite-time growth of vorticity derivatives, even under arbitrary shear modulation. The classification is obtained through an interplay between new Lyapunov functionals and Hamiltonian conservation.
Related
- Nonlinear Inviscid Damping of Couette Flow with Vorticity Perturbations Supported up to the Boundary
- Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows
- Linear Stability and Inviscid Damping of Monotone Shear Flows for 2D Compressible Euler Equations
- Linear Stability, Inviscid Damping, and Scattering for Monotone Shear Flows in 2D Ideal MHD
- On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow
BibTeX
@misc{guo2026inviscid,
title = {{Inviscid damping without derivatives near Couette flow}},
author = {Dengjun Guo and Xiaoyutao Luo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24840},
eprint = {2608.24840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24840},
}
RIS
TY - UNPB
TI - Inviscid damping without derivatives near Couette flow
AU - Dengjun Guo
AU - Xiaoyutao Luo
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2608.24840
UR - https://arxiv.org/abs/2608.24840
AB - We study the long-time dynamics near Couette flow for the 2D Euler equations in unbounded geometries. We identify a mechanism of nonlinear inviscid damping at Yudovich regularity, distinct from classical phase mixing: velocity decay driven by spatial evacuation of vorticity. The mechanism leads to a geometry-sign classification of the dynamics. In the infinite channel, small nonnegative bounded-vorticity perturbations undergo global damping without derivative assumptions. In the whole plane, small nonnegative perturbations exhibit enhanced dispersion and velocity damping, while non-positive perturbations remain confined and do not damp, even when arbitrarily small in Gevrey classes. Moreover, damping can coexist with infinite-time growth of vorticity derivatives, even under arbitrary shear modulation. The classification is obtained through an interplay between new Lyapunov functionals and Hamiltonian conservation.
ER -