  We study the gradient-flow structure of a non-Newtonian thin film equation
with power-law rheology. The equation is quasilinear, of fourth order and
doubly-degenerate parabolic. By adding a singular potential to the natural
Dirichlet energy, we introduce a modified version of the thin-film equation.
Then, we set up a minimising-movement scheme that converges to global positive
weak solutions to the modified problem. These solutions satisfy an
energy-dissipation equality and follow a gradient flow. In the limit of a
vanishing singularity of the potential, we obtain global non-negative weak
solutions to the power-law thin-film equation \begin{equation*}
  \partial_t u + \partial_x\bigl(m(u) |\partial_x^3 u - G^{\prime\prime}(u)
\partial_x u|^{\alpha-1} \bigl(\partial_x^3 u - G^{\prime\prime}(u) \partial_x
u\bigr)\bigr) = 0 \end{equation*} with potential $G$ in the shear-thinning
($\alpha > 1$), Newtonian ($\alpha = 1$) and shear-thickening case ($0 <\alpha
< 1$). The latter satisfy an energy-dissipation inequality. Finally, we derive
dissipation bounds in the case $G\equiv 0$ which imply that solutions emerging
from initial values with low energy lift up uniformly in finite time.
