偏微分方程研讨班:Stability threshold of nearly-Couette shear flows with Navier boundary conditions in 2D

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Fei Wang (Shanghai Jiao Tong University)

题  目：Stability threshold of nearly-Couette shear flows with Navier boundary conditions in 2D

时  间：2023.12.08（星期五）09:00-10:00

地  点：Zoom ID: 924 888 5804 Passcode: AMSS2022

摘 要：In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of \nu. On the other hand, the nonzero modes are assumed size O(\nu^{\frac12}) in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the inviscid damping, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework.