Stochastic stability of invariant measures: The 2D Euler equation

Abstract

In finite-dimensional dissipative dynamical systems, stochastic stability provides the selection of the physically relevant measures. That this might also apply to systems defined by partial differential equations, both dissipative and conservative, is the inspiration for this work. As an example, the 2D Euler equation is studied. Among other results this study suggests that the coherent structures observed in 2D hydrodynamics are associated with configurations that maximize stochastically stable measures uniquely determined by the boundary conditions in dynamical space.