In this paper,we study the stability for the 2-D plane Poiseuille flow(1-y^(2),0)in a channel T×(-1,1)with the Navier-slip boundary condition.We prove that if the initial perturbation for the velocity field u0 sa...In this paper,we study the stability for the 2-D plane Poiseuille flow(1-y^(2),0)in a channel T×(-1,1)with the Navier-slip boundary condition.We prove that if the initial perturbation for the velocity field u0 satisfies that||u_(0)||_(H7/2)+≤ϵ_(1)ν^(2/3)for some suitable small 0<ϵ_(1)≪1 independent of the viscosity coefficientν,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).展开更多
基金supported by the Key Project of National Natural Science Foundation of China (Grant No. 12131010)National Natural Science Foundation of China (Grant No. 12271032)+2 种基金supported by National Natural Science Foundation of China (Grant No. 12401292)the Guang Dong Basic and Applied Basic Research Foundation (Grant No. 2023A1515110500)Young Teacher Research Fund of South China Normal University (Grant No. 23KJ32)。
文摘In this paper,we study the stability for the 2-D plane Poiseuille flow(1-y^(2),0)in a channel T×(-1,1)with the Navier-slip boundary condition.We prove that if the initial perturbation for the velocity field u0 satisfies that||u_(0)||_(H7/2)+≤ϵ_(1)ν^(2/3)for some suitable small 0<ϵ_(1)≪1 independent of the viscosity coefficientν,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).
