Ricardo Rosa Federal University of Rio de Janeiro Statistical solutions have been introduced to address the evolution of probability distributions of initial conditions of the three-dimensional Navier-Stokes equations. The main issue is the lack of a global well-posedness result for the initial value problem, preventing the definition of the evolution of the measure by the transport of a semigroup. Our aim in this talk is to present a formulation, in a general abstract setting, that extends the concept and the corresponding initial value problem to other evolution equations that may suffer from a similar pathology. This is a joint work with Anne Bronzi and Cecília Mondaini.