Global classical large solutions to a 1D fluid-particle interaction model: The bubbling regime

Abstract

This paper is concerned with the 1D fluid-particle interaction model in the so-called bubbling regime which describes the evolution of particles dispersed in a viscous compressible fluid. The model under investigation is described by the conservation of fluid mass, the balance of momentum and the balance of particle density. We obtained the global existence and uniqueness of the classical large solution to this model with the initial fluid density ρ0 admitting vacuum.