Boundary Layer Theory and the ZeroViscosity Limit of the NavierStokes Equation
 E Weinan
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero. This is particularly important when boundaries are present since vorticity is typically generated at the boundary as a result of boundary layer separation. The boundary layer theory, developed by Prandtl about a hundred years ago, has become a standard tool in addressing these questions. Yet at the mathematical level, there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theory. In this article, we review recent progresses on the analysis of Prandtl's equation and the related issue of the zeroviscosity limit for the solutions of the NavierStokes equation. We also discuss some directions where progress is expected in the near future.
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 Title
 Boundary Layer Theory and the ZeroViscosity Limit of the NavierStokes Equation
 Journal

Acta Mathematica Sinica
Volume 16, Issue 2 , pp 207218
 Cover Date
 20000401
 DOI
 10.1007/s101140000034
 Print ISSN
 14398516
 Online ISSN
 14397617
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Boundary layer
 Blowup
 Zeroviscosity limit
 Prandtl’s equation
 35B05
 76D10
 Authors

 E Weinan ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, USA