Invariant measures for the non-periodic two-dimensional Euler equation
  We construct Gaussian invariant measures for the two-dimensional Euler equation on the plane. We show the existence of solution with initial conditions in the support of the measures, namely $H^\beta_{loc}(\R^2)$ with $\beta<-1$. Uniqueness and continuity of the velocity flow are proved. 
Ana Bela Cruzeiro and Alexandra Symeonides
math.AP