In this paper, we study the stability for the 2-D plane Poiseuille flow (1 − y2, 0) in a channel \(\mathbb{T}\times(-1,1)\) with the Navier-slip boundary condition. We prove that if the initial perturbation for the velocity field u0 satisfies that \(\Vert{u}_{0}\Vert_{H^{{7\over{2}}+}}\leqslant{\epsilon}_{1}\nu^{2/3}\) for some suitable small 0 < ϵ1 ≪ 1 independent of the viscosity coefficient ν, then the solution to the Navier-Stokes equations is global in time and does not transit from the plane Poiseuille flow. This result improves the result of Ding and Lin (2022).
