Jun O'Hara invented a family of knot energies Ej,p, j,p∈(0,∞). We study the negative gradient flow of the sum of one of the energies
Eα=Eα,1, α∈(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.Comment: 45 page