Rotationally symmetric p -harmonic flows from D2D2 to S2S2: Local well-posedness and finite time blow-up

We study the p  -harmonic flow from the unit disk D2D2 to the unit sphere S2S2 under rotational symmetry. We show that the Dirichlet problem with constant boundary condition 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.