In the supercritical regime of a 1D thin film equation, comparison of the initial L^{m+1} norm to that of the energy-minimizing steady state U_* determines finite-time blow-up versus global existence with diverging second moment.
Ehrhard,The spreading of hanging drops, J
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Sharp threshold for a one-dimensional thin film equation in the supercritical case
In the supercritical regime of a 1D thin film equation, comparison of the initial L^{m+1} norm to that of the energy-minimizing steady state U_* determines finite-time blow-up versus global existence with diverging second moment.