Smooth small perturbations of the explicit IPM self-similar blow-up still blow up in the same self-similar form, with a sharp regularity threshold at C^2.
W., Markfelder, S., & Titi, E
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Stable self-similar singularity formation for infinite energy solutions of the incompressible porous medium equations
Smooth small perturbations of the explicit IPM self-similar blow-up still blow up in the same self-similar form, with a sharp regularity threshold at C^2.