Lagrangian structure for two dimensional non-barotropic compressible fluids

TL;DR

This paper establishes the uniqueness of particle trajectories in two-dimensional non-barotropic compressible Navier-Stokes fluids, extending previous results for barotropic fluids and enhancing understanding of fluid dynamics in such systems.

Contribution

It introduces a Lagrangian framework for weak solutions of 2D non-barotropic compressible fluids, demonstrating trajectory uniqueness including the energy equation.

Findings

Uniqueness of particle trajectories for 2D non-barotropic fluids.

Extension of previous barotropic fluid results to non-barotropic cases.

Advancement in understanding the Lagrangian structure of compressible fluids.

Abstract

We study the lagrangian structure for weak solutions of two dimensional Navier-Stokes equations for a non-barotropic compressible fluid, i.e. we show the uniqueness of particle trajectories for two dimensional compressible fluids including the energy equation. Our result extends partially the result obtained for barotropic fluids by Hoff and Santos (2008).