Analysis of nonlocal model of compressible fluid in 1-D

TL;DR

This paper investigates a one-dimensional nonlocal compressible fluid model, establishing conditions for local and global existence of solutions with boundedness when viscosity is small.

Contribution

It proves local and global existence and boundedness of solutions for a 1-D nonlocal compressible fluid model with small viscosity.

Findings

Existence of solutions is established for small viscosity.

Solutions are shown to be uniformly bounded.

Global existence is proved under certain conditions.

Abstract

The compressible barotropic Navier-Stokes type system in monodimensional case with Neumann boundary condition given on free boundary is considered. The local and the global existence with uniformly boundedness for small viscosity coefficient is proved.