Speaker：Alexandre Boritchev (University of Lyon)
Time and Place：11 October 16:30-17:30, B1238 Zhixin Building
Title: Burgers Turbulence: a Model Case for the Kolmogorov Theory
Abstract: The Kolmogorov 1941 theory (K41) is the starting point for all models of turbulence. In particular, K41 and corrections to it provide estimates of small-scale quantities such as increments and energy spectrum for a 3D turbulent flow. However, because of the well-known difficulties involved in studying 3D turbulent flows, there are no rigorous results confirming or infirming those predictions.
Here, we consider a well-known simplified model for 3D turbulence, the 1D or multi-dimensional potential Burgers equation, with spatially smooth stochastic forcing. We give sharp estimates for small-scale quantities such as increments and energy spectrum,and then we say a few words about the dynamical features of this equation, and in particular the speed of convergence to the stationary measure.