  The propagation of zero sound in a spin-polarized Fermi gas under harmonic
confinement is studied as a function of the mean-field interactions with a
second Fermi gas. A local-density treatment is compared with the numerical
solution of the Vlasov-Landau equations for the propagation of density
distortions in a trapped two-component Fermi gas at temperature T=0.2 Tf. The
response of the gas to the sudden creation of a sharp hole at its centre is
also studied numerically.
