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Math Colloquium
Nathan Glatt-Holtz
Indiana University
Title: Some Results for the Stochastic PDEs of Fluid Dynamics

Abstract: A fundamental challenge in physics and the applied sciences is that the basic governing equations do not account for the myriad uncertainties: numerical, physical and empirical that arise in modeling. In studying the earth's oceanic-atmospheric system for example, one must contend with a vast range of spatial and temporal scales which interact in a highly nonlinear fashion. Thus, the accurate numerical simulation of realistic models remains intractable for the foreseeable future. In addition to the daunting complexity of existing models, numerous basic aspects of climate and weather are poorly understood at a physical level. Finally, unknown parameters or whole subsystems of a model may be hard to calibrate from observational data which is typically incomplete and noisy. Thus, as this important example illustrates, the basic challenge of the better understanding of complex physical systems requires the continued development of applied analysis which quantifies probabilistic uncertainties in dynamical models.

In this talk we will discuss some recent developments in the mathematical theory of stochastic versions of some basic equations in fluid dynamics,with an emphasis on the challenges of a nonlinear, state dependent noise. We will describe some recent well-posedness results for the Stochastic Navier-Stokes and Euler equations as well as for the Stochastic Primitive equations, a basic model for large scale oceanic--atmospheric dynamics. We will also discuss some parameter estimation problems for these systems. These results will highlight some analytical and numerical insights concerning the effects of different noise structures on the behavior of solutions.



Date: Monday, December 12, 2011
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Fonseca
Note: Refreshments at 4:00 pm, Wean Hall 6220