Asymptotic analysis for 1D compressible Navier–Stokes–Vlasov equations with local alignment force

Abstract

We consider the initial-boundary value problem of compressible Navier–Stokes–Vlasov equations under a local alignment regime in a one-dimensional bounded domain. Based on the relative entropy method and compactness argument, we prove that a weak solution of the initial-boundary value problem converges to a strong solution of the limiting two-phase fluid system. This work extends in some sense the previous work of Choi and Jung [Math. Models Methods Appl. Sci. 31(11), 2213–2295 (2021)], which considered the diffusive term ∂ξξfɛ in the kinetic equation. Note that the diffusion term was not considered in this paper.