Asymptotic Properties of a Class of Weak Solutions to the Navier-Stokes-Fourier System.

Many equations arising in continuum fluid dynamics do not, or at least are not known to, possess smooth solutions for general data. Therefore it is necessary to identify a larger class of "weak solutions" in order to develop a rigorous mathematical theory. Following the seminal paper of Leray [10] we introduce a class of weak solutions to the Navier-Stokes-Fourier system based on the concept of generalized derivatives (distributions). The main objective of the present paper is to illustrate the strength of the abstract theory reviewing several theoretical results on the asymptotic behavior of the weak solutions that are in good agreement with practical experiments as well as their numerical analysis.The main topics to be discussed include the following: [ABSTRACT FROM AUTHOR]