Existence and Uniqueness of Strong Solutions for a Compressible Multiphase Navier-Stokes Miscible Fluid-Flow Problem in Dimension n = 1

TL;DR

This paper proves the global existence and uniqueness of strong solutions for a one-dimensional compressible multiphase Navier-Stokes system with pressure-dependent diffusion, using a novel entropy method for control.

Contribution

It establishes the first global strong solution results for a pressure-dependent diffusion in a 1D compressible multiphase Navier-Stokes model.

Findings

Global existence and uniqueness of strong solutions in 1D

Control of density derivatives via a new entropy

Results applicable to pressure-dependent diffusion models

Abstract

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the space derivative of the density, via a new kind of entropy.