On singularities of the unsteady Prandtl’s equations
On singularities of the unsteady Prandtl’s equations
Prandtl’s equations arise in the description of boundary layers in fluid dynamics.
Solutions Ìýmight Ìýform Ìýsingularities Ìýin Ìýfinite Ìýtime, Ìýwith Ìýthe Ìýfirst Ìýreliable ÌýnumericalÌý
studies performed by Van Dommelen and Shen in the early eighties, and a rigorous proof Ìýdone ÌýlaterÌý
Ìýin Ìýthe Ìýnineties Ìýin Ìýthe Ìýseminal Ìýwork Ìýof ÌýE Ìýand ÌýEngquist Ìýin Ìýtwo dimensions. Ìý This Ìý
singularity Ìýformation Ìýis Ìýintimately Ìýlinked Ìýwith Ìýa Ìýphenomenon: the separation of the boundaryÌý
layer. ÌýThe precise structure of the singularity has however Ìýnot Ìýbeen Ìýconfirmed Ìýyet Ìý
mathematically. Ìý This Ìýtalk Ìýwill Ìýfirst Ìýdescribe Ìýthe dynamics of the inviscid model, for whichÌý
everything can be computed. ÌýThen, for the original viscous model, the second part of the talk willÌý
focus on the obtention of detailed asymptotics for the solution at a relevant particular location. Ìý
This is a collaboration with T.-E. Ghoul, S. Ibrahim and N. Masmoudi.