Dynamics of Partial Differential Equations
Volume 18 (2021)
Observable measures in partial differential equations
Pages: 279 – 292
We prove that a broad class of PDE’s including the reaction-diffusion and 2D Navier–Stokes equations have observable measures. Moreover, these measures form the minimal weak* compact subset of Borel probability measures whose basins of attraction has total Gaussian measure. To prove these results we extend the theory of observable measures  from continuous maps on compact manifolds to dissipative semiflows on Polish spaces.
SRB measure, observable measure, reaction-diffusion, Navier–Stokes, dissipative semiflow
2010 Mathematics Subject Classification
Primary 37L30. Secondary 37L40.
A la memoria del Japones, Pepe y Saponga (a gente se ve...)
Received 17 February 2020
Published 2 December 2021