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We show that for any fixed Lipschitz constant $L$, there is a time$T^*<\infty$ depending only on $L$ such that if $f:[0,T^*]\times\mathbb{R}^{2}\to [0,1]$ is a classical solution of the stable Muskat problemwith $||\nabla_x f||_{L^\infty}\leq L$, then $f$ extends uniquely to aclassical solution defined for all time. Our proof is short, quantitative, andexplicit.

Eventual regularization for the 3D Muskat problem: Lipschitz for finite time implies global existence