On a Class of Physically Admissible Variational Solutions to the Navier-Stokes-Fourier System

Abstract

The main objective of the present paper is to introduce a class of admissible variational solutions to the Navier-Stokes-Fourier system of equations based on the second law of thermodynamics. We also show that the solutions exist globally in time regardless the size of the initial data. Finally, the question of the long-time behaviour of these solutions is being addressed.