Derivation of the Euler Equations from Quantum Dynamics
  We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The second type are a number of reasonable conjectures on the statistical mechanics and dynamics of the Fermion Hamiltonian. 
Bruno Nachtergaele, Horng-Tzer Yau