In 1904, Prandtl conjectured that slightly viscous flows can be decomposed into the inviscid flows away from the boundary and a so-called Prandtl’s layer near the boundary. While various instabilities indicate the failure of the conjecture for unsteady flows (for instance, see Grenier 2000), recently with Y. Guo, we are able to prove that the conjecture holds for certain steady Navier-Stokes flows; see our paper which is to appear on Annals of PDEs.

## Archive for January, 2017

## Prandtl’s layer expansions for steady Navier-Stokes

Posted in fluid dynamics, New papers on January 31, 2017| Leave a Comment »

## Inviscid limit for Navier-Stokes in a rough domain

Posted in fluid dynamics, New papers on January 28, 2017| Leave a Comment »

In this paper with Gérard-Varet, Lacave, and Rousset, we prove the inviscid limit of Navier-Stokes flows in domains with a rough or oscillating boundary. Precisely, we study the 2D incompressible Navier-Stokes flows with small viscosity , posed on the following rough domain:

## Graduate student seminar: Kinetic theory of gases

Posted in Kinetic theory, Uncategorized on January 28, 2017| Leave a Comment »

Lat week, I gave a graduate student seminar, whose purpose is to introduce to first and second year graduate students (at Penn State) an active and beautiful topics of research, and suggest a few possible ideas for students’ presentation later in the semester. Here are slides of my talk, which focuses on Kinetic Theory of Gases, a topics that I will teach as a graduate topics course, next fall (2017).