報告題目：Prandtl-Batchelor flow on a annulus

報  告 人： 陶濤

時    間：2024年4月12日下午2：30-3：30

地    點：騰訊會議（會議号：315405838）

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.

報告人簡介：

陶濤，山東大學伟德国际1916备用网址副教授，博士畢業于中國科學院數學與系統科學研究院。主要從事不可壓縮流體方程組的研究，特别是Convex Integration在不可壓縮流體方程組中的應用(構造奇異耗散弱解)以及不可壓縮Navier-Stokes方程的粘性消失極限， 研究成果發表在Comm. Math.Phys.，J.Math.Pures Appl.，J.Funct.Anal.，SIAM J. Math. Anal.，Calc.Var.Partial Differential Equations，J.Differential Equations等國際期刊上。