Invariant measures for the non-periodic two-dimensional Euler equation

摘要

We construct Gaussian invariant measures for the 2D Euler equation on the plane. We obtain them as the weak limit of those previously considered in [1] for the torus. We show the existence of solution with initial conditions on the support of the measures. Uniqueness and continuity of the velocity flow are proved. (C) 2018 Elsevier Masson SAS. All rights reserved.