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On singularities of the unsteady Prandtl's equations Collot, Charles
Description
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.
Item Metadata
Title |
On singularities of the unsteady Prandtl's equations
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-07-03T09:00
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Description |
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.
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Extent |
50.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: New York University
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Series | |
Date Available |
2019-12-31
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0387389
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International