Introduction

The goal of this monograph is to develop a mathematical theory of open fluid systems in the framework of continuum thermodynamics.

Part I

Discusses the difference between open and closed fluid systems and introduces the Navier-Stokes-Fourier system as the mathematical model of a fluid in motion that will be used throughout the text.

Part II

A class of generalized solutions to the Navier-Stokes-Fourier system is considered in order to show existence of global-in-time solutions for any finite energy initial data, as well as to establish the weak-strong uniqueness principle.

Part III

Finally, addresses questions of asymptotic compactness and global boundedness of trajectories and briefly considers the statistical theory of turbulence and the validity of the ergodic hypothesis.