Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations

Abstract

In this paper, we study the asymptotic analysis of 1D compressible Navier-Stokes-Vlasov equations. By taking advantage of the one space dimension, we obtain the hydrodynamic limit for compressible Navier-Stokes-Vlasov equations with the pressure P (ρ) = Aρ γ (γ > 1). The proof relies on weak convergence method.

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

“…Goudon and Poupaud [39] then treated the case of a very thin spray for the particles, in which the fluid velocity is given as a fixed random field. In [36], the case of two different regimes is handled by Goudon for a coupled Burgers-Vlasov system: the asymptotic result heavily relies on the one-dimensional setting (see also [19] for a 1D compressible model).…”