Boundary layers and the vanishing viscosity limit for incompressible 2D flow. (English) Zbl 1291.35189

Lopes Filho, Milton C.

Lin, Fanghua (ed.) et al., Lectures on the analysis of nonlinear partial differential equations. Part 1. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-235-0/pbk). Morningside Lectures in Mathematics 1, 1-29 (2012).

Summary: This manuscript is a survey on results related to boundary layers and the vanishing viscosity limit for incompressible flow. It is the lecture notes for a 10 hour minicourse given at the Morningside Center of Mathematics, Academia Sinica, Beijing, PRC from 11/28 to 12/07, 2007.
The main topics covered are: a derivation of Prandtl’s boundary layer equation: an outline of the rigorous theory of Prandtl’s equation, without proofs; Kato’s criterion for the vanishing viscosity limit; the vanishing viscosity limit with Navier friction condition; rigorous boundary layer theory for the Navier friction condition and boundary layers for flows in a rotating cylinder.
For the entire collection see [Zbl 1243.35005].

MSC:

35Q30	Navier-Stokes equations
35Q31	Euler equations
76D05	Navier-Stokes equations for incompressible viscous fluids
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids

Keywords:

incompressible flow; Navier-Stokes equations; Euler equations; vorticity; boundary layers