  Global existence and long-time behavior of solutions to a family of nonlinear
fourth order evolution equations on $R^d$ are studied. These equations
constitute gradient flows for the perturbed information functionals $F[u] =
1/(2\alpha) \int | D (u^\alpha) |^2 dx + \lambda/2 \int |x|^2 u dx$ with
respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from
$\alpha=1/2$, corresponding to a simplified quantum drift diffusion model, to
$\alpha=1$, corresponding to a thin film type equation.
