Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	陶涛教授，山东大学
Inviter:	王勇副研究员
Title:	Prandtl-Batchelor flow on a annulus
Language:	Chinese
Time & Venue:	2023.12.14 11:00-12:00 腾讯会议: 697-758-288
Abstract:	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.