报告题目：Prandtl-Batchelor flow on a annulus

报 告 人：陶涛，山东大学 副教授

报告摘要：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.

报告人简介：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.，Advances in Mathematics,  J.Math.Pures Appl.，J.Funct.Anal.，SIAM J. Math. Anal.，Calc.Var.Partial Differential Equations，J.Differential Equations等国际期刊上。

报告时间：2024年11月22日 10:10-11:10

报告地点：文渊楼B536

主办单位：数学与统计学院