Corentin Le Bihan
Email: corentin[dot]le[dot]bihan[at]ulb[dot]be
Since October 2023 I have a postdoctoral position in Université Libre de Bruxelles (under the supervision of Mitia Duerinckx).
Before I was a PhD Student at ÉNS DE LYON (under the supervision of Sergio Simonella and Laure Saint-Raymond).
Research interests
My main interests (for the moment) are the derivation of kinetic equation from many body particles systems. In particular I want to understand the apparition of irreversibility in determinisitic system.
During my PhD I worked on low density limits. The particles can interact only at short distance but very strongly. Hence each collision mix a little bit the system. The typical example of such system is a large billard of N hard identical spheres, each of of diameter ε. The interesting ratio between ε and N is Nε2 = 1 (when we are in dimension 3). When the number of particles goes to infinity the system is discribe by the Boltzmann equation.
Now I work on an other interesting example is the mean-field system: the particles interact at long distance (of size 1) but weakly (the straigth of the interaction is of order 1/N). If you look at these system on time of order 1, it stays reversible (it describe by the Vlasov equation). However due to the mixing effects, the system becomes irreversible on long time (of order N). The system may be described by the Lennard-Balescu equation.
Key words
- Gas dynamic (Boltzmann equation, Landau equation)
- Low density scaling limits
- Long time behavior in mean-field scaling limits.
Here you can find my curriculum vitae.
Articles
- The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials, with Raphael Winter, published in Kinetic and Related Models, see also here
- Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions, published in Discrete and Continuous Dynamical Systems, see also here
- Long time validity of the linearized Boltzmann equation for hard spheres: a proof without billiard theory, submited, see here
- Long time validity of the linearized Boltzmann uncut-off and the linearized Landau equations from the Newton Law, submited, see here
- On essential-selfadjointness of differential operators on closed manifolds, with Y. Colin de Verdière, published in Annales de la faculté des sciences de Toulouse, Math., see also here
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