Local well-posedness for the compressible Navier-Stokes-BGK model in Sobolev spaces with exponential weight

TL;DR

This paper proves the local well-posedness of a coupled compressible Navier-Stokes and BGK model for sprays in weighted Sobolev spaces, ensuring solutions exist and are unique under certain conditions.

Contribution

It establishes the first well-posedness results for the coupled Navier-Stokes-BGK system with exponential weights in Sobolev spaces.

Findings

Existence of solutions in weighted Sobolev spaces

Uniqueness of solutions under specified conditions

Framework for analyzing complex spray dynamics

Abstract

Sprays are complex flows constituted of dispersed particles in an underlying gas. In this paper, we are interested in the equations for moderately thick sprays consisting of the compressible Navier-Stokes equations and Boltzmann BGK equation. Here the coupling of two equations is through a friction (or drag) force which depends on the density of compressible fluid and the relative velocity between particles and fluid. For the Navier-Stokes-BGK system, we establish the existence and uniqueness of solutions in Sobolev spaces with exponential weight.