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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Zhiwu Lin\, Georgia Tech\n\nAbstract: For steady two-dimensiona
l incompressible flows with a single eddy (i.e. nested closed streamlines)\
, Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishi
ng viscosity the vorticity is constant in an inner region separated from th
e 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-Batc
helor flows on a disk with the wall velocity slightly different from the ri
gid-rotation. The leading order term of the flow is the constant vorticity
solution (i.e. rigid rotation) satisfying the Batchelor-Wood formula. For a
n annulus with wall velocities slightly different from the rigid-rotation\,
we constructed a continuous curve (i.e. infinitely many) of generalized Pr
andtl-Batchelor flows\, whose leading order terms are rotating shear flows.
This is a joint work with Chen Gao\, Mingwen Fei and Tao Tao.
DTEND:20220510T220000Z
DTSTAMP:20240412T211054Z
DTSTART:20220510T210000Z
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SUMMARY:Caltech-UCLA-USC Joint Analysis and PDE Seminar: The existence of P
randtl-Batchelor flows on disk and annulus
UID:tag:localist.com\,2008:EventInstance_39889379733846
URL:https://calendar.usc.edu/event/caltech-ucla-usc_joint_analysis_and_pde_
seminar_the_existence_of_prandtl-batchelor_flows_on_disk_and_annulus
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