We study the linearization of 2D Navier-Stokes around a boundary layer , in which denotes the original coordinates for Navier-Stokes. Materials in this lecture are drawn from the joint paper(s) with Grenier and Guo (here and here).

## Archive for February, 2015

## Math 597F, Notes 6: Linear inviscid stability theory

Posted in Math 597F: topics on boundary layers on February 11, 2015| Leave a Comment »

## Math 597F, Notes 5: A few examples of 2D boundary layers

Posted in Math 597F: topics on boundary layers on February 4, 2015| Leave a Comment »

Let us give a few examples of boundary layer solutions to the Prandtl problem, derived in the last lecture. In 2D, we recall the Prandtl layer problem:

with the pressure gradient: , where denotes the tangential component of Euler flow on the boundary . Here, the tangential velocity component is an (only) unknown scalar function, and the normal velocity component is defined through the divergence-free condition. A simplest example: in the case is independent of and , any solution to the following heat problem

gives a boundary layer solution of (1) in the form . We call a solution of this form to be a shear flow.