Communications in Mathematical Sciences

Volume 11 (2013)

Number 1

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

Pages: 269 – 292

DOI: https://dx.doi.org/10.4310/CMS.2013.v11.n1.a8

Authors

Igor Kukavica (Department of Mathematics, University of Southern California, Los Angeles, Calif., U.S.A.)

Vlad Vicol (Department of Mathematics, University of Chicago, Chicago, Il., U.S.A.)

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.

Keywords

boundary layer, Prandtl equation, well-posedness, real-analyticity, matched asymptotics, inviscid limit

2010 Mathematics Subject Classification

35Q35, 76N10, 76N20

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Published 7 September 2012