On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow

W Huang, Y Sun, X Xu - arxiv preprint arxiv:2409.05104, 2024 - arxiv.org
Rotation is a crucial characteristic of fluid flow in the atmosphere and oceans, which is
present in nearly all meteorological and geophysical models. The global existence of …

The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity

F Wang, Z Zhang - arxiv preprint arxiv:2410.20404, 2024 - arxiv.org
We address a threshold problem of the Couette flow $(y, 0) $ in a uniform magnetic field
$(\beta, 0) $ for the 2D MHD equation on $\mathbb {T}\times\mathbb {R} $ with fluid viscosity …

Stability of the Couette flow for 3D Navier-Stokes equations with rotation

W Huang, Y Sun, X Xu - arxiv preprint arxiv:2412.11005, 2024 - arxiv.org
Rotation significantly influences the stability characteristics of both laminar and turbulent
shear flows. This study examines the stability threshold of the three-dimensional Navier …

Boundary driven instabilities of Couette flows

D Bian, E Grenier, N Masmoudi, W Zhao - arxiv preprint arxiv:2409.00307, 2024 - arxiv.org
In this article, we prove that the threshold of instability of the classical Couette flow in $ H^ s
$ for large $ s $ is $\nu^{1/2} $. The instability is completely driven by the boundary. The …

Viscosity driven instability of shear flows without boundaries

H Li, W Zhao - arxiv preprint arxiv:2410.23798, 2024 - arxiv.org
In this paper, we study the instability effect of viscous dissipation in a domain without
boundaries. We construct a shear flow that is initially spectrally stable but evolves into a …