Each symposium will have about 5-6 lectures of one half hour each with a discussion. The details and list of speakers in each symposium will be available later. Symposia already scheduled are listed below, together with an abstract. We plan about 10 symposia in total. However, we are open to any new and original proposition.

1. "Primitive equations for the Ocean and the Atmosphere", organized by Madalina PETCU, University of Poitier (France) Abstract
2. "Navier-Stokes equations and generalized models", organized by Luigi BERSELLI, University of Pisa (Italy) Abstract
3. "Multilevel numerical methods for flow and transport simulations in porous fractured media", organized by Jocelyne ERHEL, INRIA Rennes (France) Abstract
4. "Recent developments in Navier-Stokes equations and associated models", organized by Cherif AMROUCHE, University of Pau (France) Abstract
5. "From Freefem 2D to Freefem 3D", organized by Frederic HECHT, Pierre et Marie Curie University, Paris (France). The project FF2A3 is supported by the ANR project 08FA300-01. Abstract
6. "Fluid Dynamics for complex flows", organized by Bernard REBOURCET, CEA-DAM (France). Abstract

Abstract of Symposium 1: This symposium is dedicated to the mathematical study of the primitive equations of the ocean and of the atmosphere. The mathematical issues that are presented here are the derivation of these equations, the well-posedness of the problem under different boundary conditions, as well as the study of the stochastic primitive equations. The emphasis here goes on the primitive equations with viscosity. The theory of the primitive equations with viscosity has been developed since the early 1990s and at this point has reached a satisfactory level of comprehension. While initially considered in analogy to the Navier-Stokes equations, it was recently proved that in fact the primitive equations with viscosity are well-posed in space of dimensions 2 and 3. Top of the page

Abstract of Symposium 2 : The aim of this symposium is to bring together researchers working on fluids, with good background in the mathematical theory of the Navier-Stokes equations, but who are also focusing on related problems such as: non Newtonian fluids, Magneto-hydro-dynamic, interface problems, stochastic partial differential equations. This will give researchers the opportunity to interact with other working in not exactly in the same area and to hear about state-of-the art results and recent advances on problems related with the mathematical fluid mechanics. Top of the page

Abstract of Symposium 3: Large sparse linear systems with up to a hundred billions of unknowns arise from 3D discretizations of groundwater numerical models. Such huge problems require scalable algorithms adapted to the hierarchical memories, the variable network speeds and the parallel capacities of supercomputing architectures. Another difficulty is to deal with heterogeneity, leading to ill-conditioned systems. Multilevel approaches are one of the most effective ways of handling memory and computational requirements. They are generally based on multigrid methods or domain decomposition methods, using Schur complements, deflation techniques or Schwarz iterations. This mini-symposium investigates these issues and presents some robust, efficient and scalable algorithms. Applications to groundwater simulations illustrate the challenge and the results obtained with these algorithms. Top of the page

Abstract of Symposium 4: The minisymposium "Recent developments in Navier-Stokes equations and associated models" is devoted to the study of  some models in fluids mechanics (Oseen, Navier-Stokes) in bounded domains, in exterior domains or in half-spaces. In a related context, there are also interesting mathematical and numerical results for liquid crystal models. Top of the page

Abstract of Symposium 5: This symposium is dedicated to recent dévelopments of the 3D version of Freefem ++ that aims to compute numerical simulations of solutions of any partial differential equations. The focus will be on special applications to fluid mechanics and turbulence. Top of the page

Abstract of Symposium 6: This minisymposium is devoted to the mathematical analysis and the numerical schemes related to fluid system for complex flows. For example, the compressible Euler equations will be considered in a multimaterial framework ; they may be analysed also in the case of the low Mach number. In another direction, these equations may be coupled with laser propation system for dealing with laser-interaction problems. Top of the page