  This paper establishes the global well-posedness of the nonlinear
Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The
equation captures the mean-field behavior of a classic multiagent system for
opinion dynamics. We prove the global existence, uniqueness, nonnegativity and
regularity of the weak solution. We also exhibit a global stability condition,
which delineates a forbidden region for consensus formation. This is the first
nonlinear stability result derived for the Hegselmann-Krause model.
