On the local existence of analytic solutions to the Prandtl boundary layer equations

Igor Kukavica; Vlad Vicol

doi:10.4310/CMS.2013.v11.n1.a8

On the local existence of analytic solutions to the Prandtl boundary layer equations

Igor Kukavica, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

84 Scopus citations

Abstract

We address the local well-posedness of the Prandtl boundary layer equations. Using a new change of variables we allow for more general data than previously considered, that is, we require the matching at the top of the boundary layer to be at a polynomial rather than exponential rate. The proof is direct, via analytic energy estimates in the tangential variables.

Original language	English (US)
Pages (from-to)	269-292
Number of pages	24
Journal	Communications in Mathematical Sciences
Volume	11
Issue number	1
DOIs	https://doi.org/10.4310/CMS.2013.v11.n1.a8
State	Published - Mar 2013

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Boundary layer
Inviscid limit
Matched asymptotics
Prandtl equation
Real-analyticity
Well-posedness

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abstract = "We address the local well-posedness of the Prandtl boundary layer equations. Using a new change of variables we allow for more general data than previously considered, that is, we require the matching at the top of the boundary layer to be at a polynomial rather than exponential rate. The proof is direct, via analytic energy estimates in the tangential variables.",

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KW - Matched asymptotics

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KW - Real-analyticity

KW - Well-posedness

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On the local existence of analytic solutions to the Prandtl boundary layer equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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