Asymptotics, Numerics, Analysis 
of the network 


Sites of F2  ENS Ulm + Paris 6, X, INRIA, Lille 
URL  F2 
Team Organizer  F. Golse 
This group has been heavily involved for more than ten years in developing some of the modern analytical tools for kinetic models and conservation laws  such as smoothing by velocity averaging, dispersion and Strichartz estimates for transport equations with applications to the smoothness of solutions of the VlasovPoisson system, kinetic formulations of (systems of) conservation laws... In all satellites of the F2 group, different themes of the work program are represented, a circumstance that fostered intense cooperation, such as the working seminar on problems of geometrical optics (taskÂ 13Â of the work program) involving the group of applied mathematics at ENS Ulm, J.D. Benamou from INRIA and researchers from CEA (the French Atomic Energy Commission) organized bimonthly at ENS Ulm in 19992000. Likewise, a GDR (research network at the national level operated by CNRS, the French agency of scientific research) focussed on the modelling, mathematical analysis and scientific computing of the dynamics of charged particles (taskÂ 2Â of the work program) involved the teams from ENS Ulm, Ecole Polytechnique and Paris 6 in a significant way and promoted their interactions with industrial partners (such as CEA, Thomson...)
A traditional theme for this group is that of macroscopic limits of kinetic or particle models, with applications to kinetic schemes. This theme intersects with tasksÂ 1Â ,Â 2Â ,Â 8Â ,Â 9Â andÂ 10Â of the work program and has involved most of the participants (in particular Allaire, Bouchut, Coquel, Golse, Lucquin, Paul, Perthame, SaintRaymond) and collaborators from groups A1, G1, I1, I3, S1, S2. More classical aspects of the mathematical analysis of hyperbolic systems of conservation laws, such as described in tasksÂ 11Â andÂ 12Â of the work program, are represented mainly by LeFloch, with collaborations with group I2. Various aspects of modelling, in connection with tasksÂ 2Â ,Â 5Â ,Â 7Â ,Â 10Â andÂ 13Â of the work program currently involve Allaire, Benamou, Golse, Lucquin, Perthame, SaintRaymond), with again intensive interaction with groups D2, E1, I1, S1. Finally, the group also has a strong component of numerical analysis that ranges from the theoretical analysis of numerical schemes such as in tasksÂ 1Â andÂ 15Â to scientific computing such as in tasksÂ 5Â andÂ 16Â (involving in particular Allaire, Bristeau, Bouchut, Coquel, Despres, Perthame, and collaborations with groups D2, E1, G1, I1, I3, S1, S2 and with EDF  the French electricity agency  as industrial partner). The key scientific staff consists of
 F. Golse (TO) (ENS Ulm & Paris 6, 25%),  F. Bouchut (ENS Ulm, 25%),  T. Paul (ENS Ulm, 20% ),  C. Bardos (Paris 6, 60%),  F. Coquel (Paris 6, 30% ),  B. Despres (Paris 6, 20%),  B. Lucquin (Paris 6, 30% ),  B. Perthame (SiC) (Paris 6, 25%),  L. SaintRaymond (Paris 6, 20% ),  G. Allaire (IAB) (Ecole Poytechnique, 20% ),  P. Le Floch (Ecole Poytechnique, 20% ),  J.D. Benamou (INRIA, 20% ),  M.O. Bristeau (INRIA, 20 %)
Among the most significant publications of this group, one can quote
[1] Bressan, Alberto (I2); LeFloch, Philippe G. (F2):Â Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws.Â Indiana Univ. Math. J.Â 48Â (1999), no. 1, 4384.
[2] Bourgain, Jean; Golse, FranÃ§ois (F2); Wennberg, Bernt (S1):Â On the distribution of free path lengths for the periodic Lorentz gas.Â Comm. Math. Phys.Â 190Â (1998), no. 3, 491508.