University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Local stability of Dirac masses for a kinetic model of alignment on the sphere

Local stability of Dirac masses for a kinetic model of alignment on the sphere

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  • UserAmic Frouvelle, Université de Paris Dauphine
  • ClockMonday 21 March 2016, 16:00-17:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Amit Einav.

We consider a kinetic version of a model of alignment of particles : two particles are chosen at random and collide, their new orientation corresponding to the « average » of their initial orientations. When the initial density is sufficiently close to a Dirac mass, we prove that an energy linked to the W₂ distance is decreasing. We are able to overpass the lack of conservation of the center of mass and get the convergence of the density towards a Dirac mass, with an optimal exponential rate. The main tools are global and local estimations of the error in the spherical version of Apollonius’ formula (joint work with Pierre Degond and Gaël Raoul).

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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