Year: 2026
Type: preprint
Abstract: We study the transition threshold problem for the 2D Navier--Stokes Boussinesq equations around the Poiseuille flow on three domains: $\mathbb{T} \times \mathbb{R}$, $\mathbb{T} \times [0, \infty)$, and $\mathbb{T} \times [-1, 1]$. More precisely, we prove that if the initial perturbations of the vorticity and the temperature are assumed size $O(\min\{ν^{\fr34},μ^{\fr34},ν^{-\fr14}μ\})$ and $O(\min\{ν^{\fr94},μ^{\fr94}\})$ in an anisotropic Sobolev space respectively, then for the solution to this system, its size remains so for all time, and the nonlinear enhanced dissipation persists with a rate proportional to $O(\min\{ν^{\fr12},μ^{\fr12}\})$.
Source: arXiv (Cornell University)
Author: Zhang, Nangao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221004391