Abstract. For steady two-dimensional incompressible flows with a single eddy (i.e. nested closed streamlines), Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishing viscosity the vorticity is constant in an inner region separated from the boundary layer. 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. For an annulus with wall velocities slightly different from the rigid-rotation, we also constructed Prandtl-Batchelor flows, whose leading order terms are rotating shear flows. This is a joint work with Chen Gao, Mingwen Fei and Tao Tao.

Bio. Prof. Zhiwu Lin got his Bachelor degree in Peking University and Ph.D degree in Brown University. He is an expert in analysis on partial differential equations, in particular, for problems from fluid dynamics, kinetic theory, nonlinear waves, and stability theory. He has published many important papers in prestigious journals, such as Invention Math., Comm. Pure. Appl. Math., Arch. Ration. Mech. Anal., Comm. Math. Phys., etc. He is also on the editorial board on a few journals, such as SIAM J. Math. Anal., etc.