Mathematical and Geophysical Fluid Dynamics
February 13 to February 17, 2006
American Institute of Mathematics,
Palo Alto, California
Boris Rozovskii ,
and Joseph Tribbia
This workshop will bring together
experts in the deterministic and stochastic dynamics of fluids and
gases with experts in geosciences who work on numerical simulations
of large scale models of climate and related subsystems. The main
goal of the workshop is to facilitate transfer of recent advances
in mathematical and computational Fluid Dynamics to the geophysical
community involved in the modeling of the ocean and atmosphere,
and to stimulate new developments in both areas.
Even though fluid equations have had a long and distinguished history,
many of the fundamental mathematical questions associated with them remain
an open challenge, such as the Clay Prize problem for the Navier-Stokes
equations. In addition, there are many less famous problems which are
nevertheless very important and which involve the Navier Stokes equations,
as well as the Boussineq and Primitive equations of the oceans and the
Areas of interest for this workshop will include:
- The mathematical theory of the Boussinesq and Primitive Equations (PEs)
and related equations. Although these equations are slightly less regular
than the incompressible Navier-Stokes equations, their mathematical theory
has recently been brought to essentially the same level as that of the
Navier-Stokes equations in terms of the existence, uniqueness, and
regularity of solutions in the two-and three-dimensional cases.
- Stochastic equations of fluid dynamics. This emerging field brings
together experts from the mechanics of fluids, PDEs and stochastic
analysis. It has long been suspected that the Navier-Stokes and Euler
equations with random perturbations might serve as an important
mathematical model for the turbulent motion of a fluid with a high
Reynolds number. In addition, some stochastic versions of the Primitive
Equations have proved to be instrumental in modeling the ocean/atmosphere
interaction that is the key to understanding climate variability.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.