Giovanni Gallavotti Universita di Roma “La Sapienza”
Viscosity, reversibility, chaotic hypothesis in NS fluids
A statistical representation of viscosity in the framework of a thermodynamic formalism for the description of the stationary distributions of incompressible fluid flows. Various equations are proposed and their equivalence with the Navier-Stokes equations with cut-off N is presented as an instance of equivalence of ensembles. The cut-off N to infinity plays the role of the infinite volume limit, the viscosity the role of inverse temperature, the average enstrophy the role of the energy in thermodynamics,… In the infinite N limit the equivalence between the different descriptions is expected to be exact for the averages of large scale observables. Among the several equivalent equations some are reversible and therefore offer a different view of the viscosity in the context of the “Chaotic Hypothesis”.
Video of the lecture