On singularities of the unsteady Prandtl’s equations

On singularities of the unsteady Prandtl’s equations

-
Charles Collot, NYU
Fine Hall 322

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.