  We consider solutions to the space-homogeneous Landau equation with a general
family of interaction potentials. We prove that their Fisher information is
monotone decreasing in time. The class of interaction potentials covered by our
result includes the case of the Landau equation with Coulomb interactions. As a
consequence of the global boundedness of the Fisher information, we deduce that
solutions to the space-homogeneous Landau equation never blow up.
