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We study the $p$-harmonic flow from the unit disk $D^2$ to the unit sphere$S^2$ under rotational symmetry. We show that the Dirichlet problem withconstant boundary conditions is locally well-posed in the class of classicalsolutions and we also give a sufficient criterion, in terms of the boundarycondition, for the derivative of the solutions to blow-up in finite time.

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