  Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \in (0,
\infty)$. We study the negative gradient flow of the sum of one of the energies
$E^\alpha = E^{\alpha,1}$, $\alpha \in (2,3)$, and a positive multiple of the
length.
  Showing that the gradients of these knot energies can be written as the
normal part of a quasilinear operator, we derive short time existence results
for these flows. We then prove long time existence and convergence to critical
points.
