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

TL;DR

This paper proves the existence of global weak solutions for a coupled Navier-Stokes-Vlasov-Boltzmann system modeling a thick spray, handling breakup effects and unbounded particle velocities.

Contribution

It establishes the first global weak solution existence result for this complex coupled system with breakup effects and unbounded velocities.

Findings

Existence of global weak solutions proven

Handles breakup effects in the model

Addresses unbounded particle velocities

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.