For more information about this meeting, contact Fei Wang, Toan Nguyen, Stephanie Zerby, Mark Levi, Victor Nistor, Jinchao Xu, Ludmil Zikatanov, Chun Liu.
|Title:||Turbulent fluid flow and the inviscid limit for the stochastic Navier-Stokes equations|
|Seminar:||Computational and Applied Mathematics Colloquium|
|Speaker:||Vlad Vicol, Princeton University|
|Turbulence theory aims to make a precise connection between the ubiquitous complex patterns exhibited by fluids at high Reynolds number and the basic equations of fluid dynamics, such as the Navier-Stokes and Euler equations. Given the inherent unpredictability of individual realizations in a turbulent regime, it is crucial to develop a statistical approach. This is one of the fundamental motivations for the mathematical study of stochastic partial differential equations in the context of fluids. In particular, invariant measures provide a canonical object connecting the fluid equations to the heuristic statistical properties of turbulent flows. In this talk we discuss recent results concerning the inviscid limit of invariant measures for the 2D stochastic Navier-Stokes equations. We prove that the limiting measures are supported on bounded vorticity solutions of the 2D Euler equations, thereby answering a question posed by S.~Kuksin. We also discuss connections between these limiting measures and the statistical mechanics based predictions concerning the long-term dynamics of the 2D Euler equation.|
Room Reservation Information
|Date:||03 / 03 / 2014|
|Time:||02:30pm - 03:30pm|