Asymptotics, Numerics, Analysis 
of the network 


Sites of F1  Dauphine + Orsay, ENSCachan, CERMICS, Versailles, Evry, OrlÃ©ans, Tours 
URL  http://www.ceremade.dauphine.fr/~dolbeaul/Hyke/F1.html 
Team Organizer  J. Dolbeault 
The F1 team is made of several groups belonging to universities (Dauphine, Orsay, Evry, OrlÃ©ans, Versailles), schools and research centers ( Cachan, CERMICS), which have been very active in the study of partial differential equations arising from physics.
The main resarch areas of the F1 team that are concerned with the project (tasksÂ 2Â ,Â 3Â ,Â 5Â ,Â 6Â ,Â 7Â ,Â 8Â ,Â 9Â ,Â 10Â ,Â 12Â ,Â 13Â ,Â 15Â ,Â 16Â ) are:
Kinetic EquationsÂ : existence and regularity theory (including the case of Boltzmann and Landau equations, and collisional or dispersive models for bosons), kinetic formulations and relaxation methods for systems of conservation laws, gases without pressure, numerical methods for collision operators and multiscale analysis of models of charged particles, entropy dissipation methods for the long time asymptotics of diffusive systems,
Fluid Dynamics :Â weak solutions for fluid mechanics and fluidstructure interactions, fluids with polymers,Â dirtyÂ fluids (with particles or agregates), particle and finite element methods for compressible or incompressible fluids.
PDEs of Quantum Mechanics :Â stationary or time dependent equations for quantum chemistry, large time, semiclassical and thermodynamical (crystals) limits, semiclassical limits and homogenization (Wigner measures, WKB analysis), eigenvalue crossings, geometric optics for very high frequency waves in inhomogeneous media, HamiltonJacobi type equations, stability of nonlinear dispersive problems, numerical methods and relativistic models for quantum chemistry.
The team has a strong experience of collaborations and training through bilateral agreements and european networks (TMR). Through already existing collaborations, it is expected to contribute in the development of entropy dissipation techniques (A1, D1, S1 Wroclaw, E1 Bilbao), in stability analysis (F3 Toulouse, F4 Rennes, E2), in the derivation of linear kinetic equations from particle models with obstacles (I1 Roma"La Sapienza"), in the study of granular media (I1 Roma"La Sapienza", I2, I3 and I3 Politecnico di Milano, S1 Karlstad), of multiscale phenomena for charged particles systems (A1, F3), of fluid mechanics and fluidstructure interactions (F4, E1 Bilbao, E2), of collisional models for sprays and of fluids with polymers andÂ dirtyÂ fluids (F2). The group should also play a leading role in the study of equations of quantum mechanics (A1, F3), of HamiltonJacobi equations and nonlinear geometric optics methods (G1), with possible applications to control theory (F4 Rennes, E1 Madrid). Both theoretical and numerical (CERMICS, OrlÃ©ans) points of view are well represented.
The key scientific staff consists of the following members (in brackets: project involvement in percentage of full time employment):
 J. Dolbeault (TO) (Paris IXDauphine, 30%)  P. L. Lions (Paris IXDauphine, 10%)  M.J. Esteban (SAB) (Paris IXDauphine, 25%)  E. Sere (Paris IXDauphine, 20%)  I. Catto (Paris IXDauphine, 20%)  P. Gerard (Paris Sud Orsay, 30%)  I. Gallagher (Paris Sud Orsay, 30%)  N. Burcq (Paris Sud Orsay, 20%)  L. Desvillettes (ENS Cachan,30%)  C. Le Bris (ENPC, 20%)  S. Mischler (Versailles, 30%)  S. MasGallic (IAB) (Evry, 30%)  L. Corrias (Evry, 30%)  S. Cordier (Orleans, 30%)  F. James (Orleans, 30%)  G. Barles (Tours, 30%)
The two most significant publications for the IHP project are the following:
[1] L. Desvillettes (F1), C. Villani (F4),Â On the trend to global equilibrium in spatially inhomogeneous entropydissipating systems. Part I : The linear FokkerPlanck equation,Â Comm. Pure Appl. Math.Â 54Â (2001), no. 1, 142.
[2] I. Catto, C. Le Bris, P.L. Lions,Â On the thermodynamic limit of HartreeFock type models,Â to appear in Ann. Inst. H. PoincarÃ©, Anal. Non LinÃ©aire, 2001.