Abstract
The long-time nonlinear evolution of generic initial perturbations in stable Vlasov plasma and two-dimensional (2D) ideal fluid is studied. Even without dissipation, these systems relax to new steady states (Landau damping). The asymptotic damping laws are found to be algebraic, such as ${t}^{\ensuremath{-}1}$ for 1D plasma potential, or ${t}^{\ensuremath{-}5/2}$ for evolving stream function in a flow with nonvanishing shear. The rate of the relaxation is fast so that phase-space/fluid-element displacement in certain directions is uniformly small, implying that decaying Vlasov and 2D fluid turbulences are not ergodic.
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