Global well-posedness of one-dimensional compressible Navier-Stokes-Vlasov system

TL;DR

This paper proves the global existence and uniqueness of weak solutions for a one-dimensional coupled fluid-particle system involving compressible Navier-Stokes and Vlasov equations, applicable to both periodic and real line domains.

Contribution

It establishes the first comprehensive global well-posedness results for the one-dimensional compressible Navier-Stokes-Vlasov system with general initial data.

Findings

Global existence of weak solutions is proved.

Uniqueness of solutions is established.

Solutions become classical for regular initial data.

Abstract

A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the one-dimensional compressible Navier-Stokes-Vlasov system and establish the global existence and uniqueness of the weak solution for general initial data in either spatial periodic domain or spatial real line, which is shown to be a classical solution for regular initial data.