Stability for the 2-D plane Poiseuille flow in finite channel
Abstract
In this paper, we study the stability for 2-D plane Poiseuille flow (1-y2,0) in a channel T× (-1,1) with Navier-slip boundary condition. We prove that if the initial perturbation for velocity field u0 satisfies that \|u0\|H72+ ≤ ε1 2/3 for some suitable small 0<ε1 1 independent of viscosity coefficient , 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 DL1 from 3/4 to 2/3.
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