ncts

Prandtl’s equations arise in the description of boundary layers in fluid dynamics. Solutions might form singularities in finite time, leading to a phenomenon called separation. The first reliable numerical studies were performed by Van Dommelen and Shen in the early 80's, and a rigorous proof of the existence of singularities was done later in the seminal work of E and Engquist in the 90's. However, 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.

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