  We show, by the means of several examples, how we can use Gibbs measures to
construct global solutions to dispersive equations at low regularity. The
construction relies on the Prokhorov compactness theorem combined with the
Skorokhod convergence theorem. To begin with, we consider the non linear
Schr\"odinger equation (NLS) on the tri-dimensional sphere. Then we focus on
the Benjamin-Ono equation and on the derivative nonlinear Schr\"odinger
equation on the circle. Next, we construct a Gibbs measure and global solutions
to the so-called periodic half-wave equation. Finally, we consider the cubic 2d
defocusing NLS on an arbitrary spatial domain and we construct global solutions
on the support of the associated Gibbs measure.
