Speaker
Description
To derive a macroscopic description of a system (in terms of
hydrodynamical fields), starting from a microscopic one (in terms of
interacting particles), the usual route introduces an intermediate
kinetic equation, and takes advantage of the difference of time scales
between fast and slow modes to set up a Chapman-Enskog expansion. When
finite size effects are important at the macroscopic level, they are
taken into account by adding a noise on the hydrodynamical equations,
often in an empirical way. We will explain how this whole procedure can
be carried out at the level of large deviations functionals, taking the
classical example of incompressible Navier-Stokes equations.
In the compressible case, the macroscopic equations are ballistic at
leading order. The large deviation structure is more complicated and we
will describe a first attempt to understand it using simpler 1D models.
