at the

American Institute of Mathematics, Palo Alto, California

organized by

Boris Rozovskii , Roger Temam, and Joseph Tribbia

This workshop, sponsored by AIM and the NSF, 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 atmosphere.

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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

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