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.©2003 B. Nachtergaele and H.-T. Yau. This article may be reproduced in its entirety for non-commercial purposes.Research partially supported by NSF # DMS-0070774.Research partially supported by NSF # DMS-0072098, the Veblen Fund from the Institute for Advanced Study and a Fellowship from the MacArthur Foundation.