Rotationally symmetric p-harmonic flow from D^2 to S^2: local well-posedness and finite time blow-up

We study the p-harmonic flow from the unit disk D2 to the unit sphere S2 under rotational symmetry. We show that the Dirichlet problem with constant boundary conditions is locally well-posed in the class of classical solutions and we also give a sufficient criterion, in terms of the boundary condition, for the derivative of the solutions to blow-up in finite time.