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



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.)


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.


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

2010 Mathematics Subject Classification

35Q35, 76N10, 76N20

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