Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate

In this paper, we study the transition threshold problem for 2-D Navier-Stokes equations around Poiseuille flow (1?y2,0) in a finite channel with Navier-slip boundary condition. Based on resolvent estimates linearized operator flow, first establish enhanced dissipation sharp decay rate e?c?t. As an application, prove that if initial perturbation of vorticity satisfies??0?L2?c0?34 some small constant c0>0 independent viscosity ?, then solution does not away from any time.