1 报告题目：Prandtl-Batchelor flow on a annulus
主讲人：陶涛（山东大学）
时间：2023年11月30日15:30-16:30
腾讯会议号：914359892
摘要：For steady two-dimensional flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the limit of vanishing viscosity, the vorticity is constant in an inner region separated from the boundary layer. In this talk, we consider the generalized Prandtl-Batchelor theory for the forced steady Navier-Stokes equation on an annulus. First, we observe that in the vanishing viscosity if forced steady Navier-Stokes solutions with nested closed streamlines on an annulus converge to steady Euler flows which are rotating shear flows, then the Euler flows and the external force must satisfy some relation. We call solutions of steady Navier-Stokes equations with the above property Prandtl-Batchelor flows. Then, by constructing higher order approximate solutions of the forced steady Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on an annulus with the wall velocity slightly different from the rigid-rotation.
个人简介：陶涛, 山东大学数学学院副教授，博士毕业于中国科学院数学与系统科学研究院。主要从事不可压缩流体方程组的研究，特别是Convex Integration在不可压缩流体方程组中的应用(构造奇异耗散弱解)以及不可压缩Navier-Stokes方程的粘性消失极限, 研究成果发表在Comm. Math.Phys.，J.Math.Pures Appl.，J.Funct.Anal.，SIAM J. Math. Anal.，Calc.Var.Partial Differential Equations，J.Differential Equations等期刊上。
2 报告题目：Global well-posedness of some 3D incompressible viscous fluid system.
主讲人：朱宁（山东大学）
时间：2023年11月30日16:30-17:30
腾讯会议号：914359892
摘要：In this talk, we will first review the important classical results for the 3D Navier-Stokes system. Then we will discuss two important spacial initial data which are called “well-prepared” data and “ill-prepared” data, and give some related results. In the next part, we will present some recent result that establishes the global well-posedness of the 3D Navier-Stokes system providing only one unidirectional derivative to be small. Finally we show the extension of relevant results in inhomogeneous Navier-Stokes equations and MHD system.
个人简介：朱宁，山东大学数学学院副研究员。2020年于北京师范大学获得博士学位，2021-2022年于北京大学从事博士后研究。主要研究方向为流体力学方程的适定性理论，在Calc. Var. Partial Differential Equations，J. Nonlinear Sci.，Nonlinearity等学术杂志上发表论文多篇。
