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math.AP2020
Cauchy theory for general Vicsek models in collective dynamics and mean-field limit approximations
Marc Briant, Antoine Diez, Sara Merino-Aceituno
In this paper we provide a local Cauchy theory both on the torus and in the whole space for general Vicsek dynamics at the kinetic level. We consider rather general interaction ker…
math.AP2020
Rigorous derivation of the Fick cross-diffusion system from the multi-species Boltzmann equation in the diffusive scaling
Marc Briant, Bérénice Grec
We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann in a rigorous manner in Sobolev spaces. To this end, we f…