Global derivation of a Boussinesq-Navier-Stokes type system from fluid-kinetic equations

Abstract

We study a hydrodynamic limit of the Vlasov-Navier-Stokes system with external gravity force, following the framework introduced by Han-Kwan and Michel in [44]. We answer a question raised in the latter concerning the derivation of a Boussinesq-Navier-Stokes type system for arbitrarily large times, starting from the previous fluid-kinetic system. To do so, we consider a particular spatial geometric setting corresponding to the half-space case. Our proof is based on an absorption effect at the boundary which leads to crucial decay in time estimates. Contents

Large coupling in a FitzHug-Nagumo neural network: quantitative and strong convergence results

“…More generally, this result is related to other concentration phenomena occurring in various kinetic models. We mention [23], where the authors go through the asymptotic analysis of a collisionless and non-diffusive Vlasov-type equation undergoing strong local alignment forces, and also [19] and [16], where the authors study the large time behavior of a Vlasov-Navier-Stokes system respectively in bounded (with periodic boundary conditions) and unbounded domain.…”