Title: New Well-Posedness Results for the Stochastic Equations of Geophysical
Fluid Dynamics

Speaker:  Nathan Glatt-Holtz 
Indiana University

Abstract: The Primitive Equations are widely regarded as a
fundamental description of geophysical scale uid ow. They provide the
analytical core of large General Circulation Models (GCMs) that are at
the forefront of numerical simulations of the earths ocean and
atmosphere. In view of the wide progress made in com- putation the
need has appeared to better understand and model some of the
uncertainties which are contained in these GCMs. This is the so called
prob- lem of parametrization. Besides all of the physical forms of
parametrization, stochastic modeling has appeared as one of the major
modes in the contempo- rary developement of the eld. In this context
there is a clear need to better understand the numerical and
analytical underpinnings of stochastic partial dif- ferential
equations. 

Although the study of well-posedness for nonlinear
stochastic evolution sys- tems such as the Navier-Stokes equations
goes back to the 1970s, many basic questions are still open. In
particular the case of nonlinear multiplicative noise presents
challenging problems since the equations are not easily transformed
into a more classical random PDE. In this talk we introduce some
recently developed techniques which may be used to circumvent the
diculty of compactness. In particular our techniques have led to novel
local and global existence results con- cerning pathwise solutions for
both the Navier-Stokes and Primitive Equations.  This is joint work
with M. Ziane and R. Temam.