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This content will become publicly available on January 11, 2026

Title: Stability threshold of nearly-Couette shear flows with Navier boundary conditions in 2D
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $$\mathbb{T} \times [-1,1]$$, supplemented with Navier boundary conditions $$\omega|_{y = \pm 1} = 0$$. Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of $$\nu$$. On the other hand, the nonzero modes are assumed size $$O(\nu^{\frac12})$$ in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the \textit{inviscid damping}, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework.  more » « less
Award ID(s):
2108633
PAR ID:
10597650
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Communications in Mathematical Physics
ISSN:
1432-0916
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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