Existence of global weak solutions for the Navier-Stokes-Vlasov-Boltzmann equations

2016/09/21 by Lei Yao, Cheng Yu, Yao, Lei +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1609.06620

openalex publication_date 2016/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A moderately thick spray can be described by a coupled system of equations consisting of the incompressible Navier-Stokes equations and the Vlasov-Boltzmann equation. We investigate this kind of mathematical model in this paper. In particular, we study the initial value problem for the Navier-Stokes-Vlasov-Boltzmann equations. The existence of global weak solutions is established by a weak convergence method. The interesting point of our main result is to handle the model with some breakup effects while the velocity of particles is in the whole space.

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• Hydrodynamic limit for compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force

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