Uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force

TL;DR

This paper proves the uniqueness of weak solutions for the 3D compressible Navier-Stokes equations with potential force, using a Lagrangian approach to analyze solution dependence on initial data and steady states.

Contribution

It introduces a Lagrangian framework to establish uniqueness and continuous dependence of weak solutions on initial conditions for the compressible Navier-Stokes equations with potential force.

Findings

Weak solutions are unique under the given conditions.

Solutions depend continuously on initial data and steady states.

The Lagrangian approach effectively compares different solutions.

Abstract

We prove uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We make use of the Lagrangean framework in comparing the instantaneous states of corresponding fluid particles in two different solutions. The present work provides qualitative results on how the weak solutions depend continuously on initial data and steady states.