Speaker: 陶涛副教授，山东大学

Inviter: 韩丕功

Title: Prandtl–Batchelor Flows on a Disk

Language: Chinese

Time & Venue: 2024.11.28 15:00-16:00 腾讯会议：563-859-808

Abstract: For steady two-dimensional flows with a single eddy (i.e. nested closed streamlines), Prandtl (Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg, 1905) and Batchelor (J Fluid Mech 7(1):177–190, 1956) proposed that in the limit of vanishing viscosity the vorticity is constant in an inner region separated from the boundary layer. In this paper, by constructing higher order approximate solutions of the 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 a disk with the wall velocity slightly different from the rigid-rotation. The leading order term of the flow is the constant vorticity solution (i.e. rigid rotation) satisfying the Batchelor–Wood formula.