Analysis Seminar

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On singularities of the unsteady Prandtl’s equations and related problems

Speaker: Charles COLLOT, Courant

Location: Warren Weaver Hall 1302

Date: Thursday, December 6, 2018, 11 a.m.

Synopsis:

Prandtl’s equations arise in the description of boundary layers
in fluid dynamics. Solutions might blow up in finite time, with the first
reliable numerical studies performed by Van Dommelen and Shen, and a
rigorous proof done later in the seminal work of E and Engquist in two
dimensions. The precise structure of the singularity has not been
confirmed yet mathematically. The main result presented in the talk will
concern the obtention of detailed asymptotics for singular solutions of a
reduced problem. This result will be related to the singularities of the
inviscid Prandtl’s equations, since the viscosity should be asymptotically
negligible during blow-up. A related result on Burgers equation with transverse viscosity
will also be presented. This is a collaboration with T.-E. Ghoul, S.
Ibrahim and N. Masmoudi.