Abstract
We exhibit a new decomposition of the nonlinearity for the Muskat equation and use it to commute Fourier multipliers with the equation. This allows to study solutions with critical regularity. As a corollary, we obtain the first well-posedness result for arbitrary large data in the critical space H˙2(R2)∩W1,∞(R2). Moreover, we prove the existence of solutions for initial data which are not Lipschitz.
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