1.报告题目：Vanishing viscosity limit of the stationary Navier-Stokes equations in an expanding annulus

报告人：潘星宏 副研究员

邀请人：严远祥

报告时间：11月6日下午15:00-16:00

报告地点：白云校区图书馆719达之学堂

报告摘要：In this paper, we establish vanishing viscosity limit of the 2D stationary Navier-Stokes equations in an expanding annulus with a fixed width. The flow is subjected to a large perturbation of a rotation of rigid body at one boundary and stays at rest at another boundary. Due to this different boundary condition setting, the boundary layer effects are different near the interior and exterior boundaries, which result in different thickness of boundary layer and different leading order boundary layer equations. We will construct an approximate solution to this 2D Navier-Stokes equations by using higher order asymptotic approximation and show the validity of the boundary layer expansion. The leading order of the Euler solution is the Taylor-Couette flow $\left(Ar+B\frac{1}{r}\right)e_\theta$ for some suitable constant $A$ and $B$, which is determined by using the principle of the Prandtl-Batchelor theory. The perturbation of the tangential velocity becomes large as the annulus expands, which causes heavy difficulties when we show the convergence of the approximate solution. Variously weighted energy estimates up to third-order derivatives of the error solution are constructed to close the energy of the nonlinear system. This is a joint work with Chuankai Zhao and Jianfeng Zhao.

报告人简介： 潘星宏,南京航空航天大学数学学院副研究员，入选2018年江苏省“双创博士”人才计划，主持省部级基金项目一项,国家自然科学基金两项。主要研究Navier-Stokes方程相关问题。目前, 在ARMA, JFA, SIAM JMA, JDE, CVPDE, SCI MATH等杂志发表多篇论文。

2.报告题目：Some applications of dispersive effects in decay estimates of fluid dynamics

报告人：李扬 副教授

邀请人：严远祥

报告时间：11月6日下午16:10-17:10

报告地点：白云校区图书馆719达之学堂

报告摘要：In this talk, we focus on several applications of dispersive effects in decay estimates of fluid dynamics. First, we consider the decay estimates of global solutions to 3D anisotropic Boussinesq equations with only horizontal dissipation. Apart from the expected 2D heat decay, we reveal the additional dispersive decay rates due to the hydrostatic equilibrium. We also reveal the enhanced dissipation of the third component of velocity field, essentially due to the divergence-free condition. Second, we consider the decay estimates of global solutions to 3D rotating Navier-Stokes equations. By developing delicate estimate for the oscillatory integral resulting from the Coriolis force, we prove the sharp decay estimate of velocity field from above and below. Finally, we mention the extension to rotating MHD equations.

报告人简介：李扬，安徽大学数学科学学院副教授.研究领域为流体力学中的偏微分方程。主持国家自然科学基金青年项目、面上项目与安徽省自然科学基金面上项目，在Int. Math. Res. Not., SIAM J. Numer. Anal., Calc. Var. PDE, SIAM J. Math. Anal., Bull Lond. Math Soc. IMA J. Numer. Anal., Nonlinearity, J. Differential. Equations.等期刊发表论文20余篇。