Tuesday, May 10, 2022 at 2:00pm to 3:00pm
Zhiwu Lin, Georgia Tech
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 constructed a continuous curve (i.e. infinitely many) of generalized Prandtl-Batchelor flows, whose leading order terms are rotating shear flows. This is a joint work with Chen Gao, Mingwen Fei and Tao Tao.
Meeting ID: 961 4551 5329
After the talks we will move to this room (Meeting ID 959 7390 9517, passcode 701059) for an informal chat with the speakers.