Lagrangian structure for two dimensional non-barotropic compressible fluids

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).