Singularity formation in the incompressible Euler equation in finite and infinite time

TD Drivas, TM Elgindi - EMS Surveys in Mathematical Sciences, 2023 - ems.press
Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …

Nonlinear inviscid dam** near monotonic shear flows

AD Ionescu, H Jia - ar** near the Couette flow in a channel
AD Ionescu, H Jia - Communications in Mathematical Physics, 2020 - Springer
We prove asymptotic stability of the Couette flow for the 2D Euler equations in the domain T
* 0, 1 T× 0, 1. More precisely we prove that if we start with a small and smooth perturbation …

On the relation between enhanced dissipation timescales and mixing rates

MC Zelati, MG Delgadino… - Communications on Pure …, 2020 - Wiley Online Library
We study diffusion and mixing in different linear fluid dynamics models, mainly related to
incompressible flows. In this setting, mixing is a purely advective effect that causes a transfer …

Stability threshold of two-dimensional Couette flow in Sobolev spaces

N Masmoudi, W Zhao - Annales de l'Institut Henri Poincaré C …, 2022 - content.ems.press
We study the stability threshold of the two-dimensional Couette flow in Sobolev spaces at
high Reynolds number Re. We prove that if the initial vorticity in satisfies kin. 1/kH Ä" Re 1 …

Transition threshold for the 2-D Couette flow in a finite channel

Q Chen, T Li, D Wei, Z Zhang - Archive for rational mechanics and …, 2020 - Springer
In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations
around the Couette flow (y, 0) at high Reynolds number Re in a finite channel. We develop a …

Transition threshold for the 3D Couette flow in Sobolev space

D Wei, Z Zhang - Communications on Pure and Applied …, 2021 - Wiley Online Library
In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at
high Reynolds number Re. It was proved that if the initial velocity v 0 satisfies for some c 0> …

[BOEK][B] Transition threshold for the 3D Couette flow in a finite channel

Q Chen, D Wei, Z Zhang - 2024 - ams.org
In this paper, we study nonlinear stability of the 3D plane Couette flow $(y, 0, 0) $ at high
Reynolds number ${Re} $ in a finite channel $\mathbb {T}\times [-1, 1]\times\mathbb {T} $. It …

Stability of Couette flow for 2D Boussinesq system with vertical dissipation

W Deng, J Wu, P Zhang - Journal of Functional Analysis, 2021 - Elsevier
This paper establishes the nonlinear stability of the Couette flow for the 2D Boussinesq
equations with only vertical dissipation. The Boussinesq equations concerned here model …