Non UBC
DSpace
Charles Collot
2019-12-31T09:19:41Z
2019-07-03T09:00
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. We will describe how to compute the maximal time of existence of a solution, study certain self-similar profiles, and show that one in particular gives rise to the generic formation of the van Dommelen and Shen singularity. 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.
https://circle.library.ubc.ca/rest/handle/2429/73028?expand=metadata
50.0 minutes
video/mp4
Author affiliation: New York University
Banff (Alta.)
10.14288/1.0387389
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Partial Differential Equations, Fourier Analysis
On singularities of the unsteady Prandtl's equations
Moving Image
http://hdl.handle.net/2429/73028