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 might form singularities in finite time, with the first reliable numerical
studies performed by Van Dommelen and Shen in the early eighties, and a rigorous proof done later
in the nineties in the seminal work of E and Engquist in two dimensions. This
singularity formation is intimately linked with a phenomenon: the separation of the boundary
layer. The precise structure of the singularity has however not been confirmed yet
mathematically. This talk will first describe the dynamics of the inviscid model, for which
everything can be computed. Then, for the original viscous model, the second part of the talk will
focus on the obtention of detailed asymptotics for the solution at a relevant particular location.
This is a collaboration with T.-E. Ghoul, S. Ibrahim and N. Masmoudi.