Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions

The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general collision kernels. The key point is the uniform estimate of the Sobolev norm on the global solutions to the Boltzmann equation.Comment: 21 page

Energy spread and current-current correlation in quantum systems

We consider energy (heat) transport in quantum systems, and establish a relationship between energy spread and energy current-current correlation function. The energy current-current correlation is related to thermal conductivity by the Green-Kubo formula, and thus this relationship allows us to study conductivity directly from the energy spread process. As an example, we investigate a spinless fermion model; the numerical results confirm the relationship.Comment: 5 pages, 2 figure