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AMCS Seminar | Subcritical Transition in the 3D Couette Flow

Start Date: March 28, 2016
End Date: March 28, 2016



By Professor Nader Masmoudi ( Courant Institute of Mathematical Sciences at New York University )



We discuss the dynamics of small perturbations of the plane, periodic Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number. For sufficiently regular initial data, we determine the stability threshold for small perturbations and characterize the long time dynamics of solutions near this threshold. For rougher data, we obtain an estimate of the stability threshold which agrees closely with numerical experiments. The primary linear stability mechanism is an anisotropic enhanced dissipation resulting from the mixing caused by the large mean shear; the main linear instability is a non-normal instability known as the lift-up effect. Understanding the variety of nonlinear resonances and devising the correct norms to estimate them form the core of the analysis we undertake. Joint work with Pierre Germain and Jacob Bedrossian


Biography: Nader Masmoudi received his degrees in Mathematics from  the École Normale Supérieure Paris (1996) and his PHD from  Paris Dauphine University (1999)  and his HDR in 2000.  He won the gold medal at the International Mathematic Olympiads in 1992, was 1st at the Concours of École Normale Supérieure and Ecole Polytechnique  in 1994, and won a  Presidential prize in Tunisia in 1994.  In 2002 he was the recipient of the Sloan Fellowship and in 2010 together with Kenji Nakanishi was awarded the prize for best paper in the Annales de I’Institut Henri Poincaré (C) Analyse Non Linéaire.  He received a Senior  Clay Math Scholar in the fall 2014.  He received  a chair of excellence from the Foundation Sciences Mathématiques de Paris from 2016-2018. He is currently a Professor in the Courant Institute of Mathematical Sciences at New York University.


More Information:

For more info contact: Dr. Saber  Trabelsi; email: Saber.Trabelsi@kaust.edu.sa

Date: Monday 28th March 2016
Time: 16:00 - 17:00
Location: Building 1, Level 3 Room 3422
Refreshmentswill be available at 15:45