  We review some recent results on the long time dynamics of solutions to the
Gross-Pitaevskii equation governing non-trapped dipolar Quantum Gases. We
describe the asymptotic behaviours of solutions for different initial
configurations of the initial datum in the energy space, specifically for data
below, above, and at the Mass-Energy threshold. We revisit some properties of
powers of the Riesz transforms by means of the decay properties of the heat
kernel associated to the parabolic biharmonic equation. These decay properties
play a fundamental tool to establish the dynamical features of the solutions to
the equation.
