Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations

Nangao Zhang

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arXiv · 2610.07598

Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations

Nangao Zhang

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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 $O(\min\{ν^{\fr12},μ^{\fr12}\})$.

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Nangao Zhang. 2026-10-06. Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations. https://arxiv.org/abs/2610.07598

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