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.
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.