  A class of nonlinear Fokker-Planck equations with superlinear drift is
investigated in the $L^1$-supercritical regime, which exhibits a finite
critical mass. The equations have a formal Wasserstein-like gradient-flow
structure with a convex mobility and a free energy functional whose minimising
measure has a singular component if above the critical mass. Singularities and
concentrations also arise in the evolutionary problem and their finite-time
appearance constitutes a primary technical difficulty. This paper aims at a
global-in-time qualitative analysis with main focus on the isotropic case,
where solutions will be shown to converge to the unique minimiser of the free
energy as time tends to infinity. A key step in the analysis consists in
properly controlling the singularity profiles during the evolution. Our study
covers the 3D Kaniadakis--Quarati model for Bose--Einstein particles, and thus
provides a first rigorous result on the continuation beyond blow-up and
long-time asymptotic behaviour for this model.
