Stochastic PDE and Models of Turbulence
During the 2002-2003 academic year IAS conducted a program in statistical models of turbulence. Weinan E and Gregory Falkovich were in residence for the year, and in related areas, John Ball was also at the Institute.
Although the problem of 3 dimensional turbulence has been extensively studied over the past century, our mathematical understanding of important issues such as regularity, intermittencey and coherent structures is still primitive.
The year's program focused on more tractable models which share some of the features believed to occur in 3D turbulence. Over the past few years there has been a surge of interest in such models which include, avection of a passive scalar, and randomly driven Burgers. The main purpose of this program at IAS was to bring people from mathematics, physics and fluid mechanics communities to continue this work and to explore more realistic turbulence problems, such as 2D turbulence and wave turbulence. The minimum goal was to crystalize the mathematical formulation of the problem, the expected result, and identify critical obstacles where numerical computations and simplified models might help. A second goal was to examine the recent progress on analysis of invariant measures for nonlinear PDEs, and extend them to physically realistic situations.