Ergodicity in Nonlinear Stochastic Partial Differential Equations with Applications in Turbulent Geophysical Flows
8 – 12 January 2018
Turbulence in fluids is a fundamental phenomenon of classical mechanics which remains poorly understood, both at the level of basic theory, for example in the study of convection, and in vital areas of application, notably in geology and astrophysics. Since our understanding of turbulence has an essentially statistical character, and given the ever growing torrent of data corrupted by measurement error which we would like incorporate into our models, there is a need for novel stochastic methods applicable to the partial differential equations (PDEs) of fluid dynamics. On the other hand, the investigation of turbulence provides a vital source for novel developments at the frontiers of probability theory, statistical inference, and in the analysis of a broad class of deterministic and stochastic PDEs. A powerful framework for the analysis of turbulence is provided by the stationary and ergodic theory for infinite dimensional stochastic dynamical systems. During the research in peace event, we will work on development of novel theory for stochastic PDEs and other Markovian systems in order to solve interrelated problems concerning the analysis and measurement of turbulent flows. Specifically, we will pursue the following research objectives: Heat transport in stochastic models of turbulent convection, Fast oscillation/rotation limits, and Ergodic properties in the presence of randomly perturbed boundary conditions.


Nathan Glatt-Holtz (Tulane University)
Juraj Foldes (University of Virginia)