PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephanie Zerby, Chun Liu.

Title:On the inviscid limit and stability of boundary layers of Navier-Stokes
Seminar:Department of Mathematics Colloquium
Speaker:Toan Nguyen, Penn State University
Abstract:
I will overview several recent results concerning the inviscid limit and stability / instability of boundary layers in fluid dynamics (precisely, for 2D incompressible Navier-Stokes equations). These issues are very classical: in fact, there are major works by prominent physicists such as Lord Rayleigh, W. Orr, A. Sommerfeld, Tollmien, C.C. Lin, among others, on the subject, using the spectral analysis and the Fourier normal mode theory. Physicists are interested in the estimation of the critical Rayleigh number (typically, very large) for laminar flows as well as the transition from laminar to turbulent flows. One of the results that I will discuss is to rigorously prove that there is always a non-empty range of wave numbers and Reynolds numbers between which generic laminar boundary layer flows are spectrallly unstable, despite the fact that at the infinite Reynolds number, the profiles are stable. The instability is therefore due to the presence of viscosity! Next, we use this instability result to show that boundary layer expansions in the inviscid limit are generally invalid. We also make a formal link of our construction with the multi-layer analysis and the classical Kato's criterium for the validity of the inviscid limit. Several other significant progresses in the subject will also be briefly discussed. This talk is intended to be accessible to graduate students.

Room Reservation Information

Room Number:MB114
Date:10 / 09 / 2014
Time:03:30pm - 04:20pm