  We paralinearize the Muskat equation to extract an explicit parabolic
evolution equation having a compact form. This result is applied to give a
simple proof of the local well-posedness of the Cauchy problem for rough
initial data, in homogeneous Sobolev spaces $\dot{H}^1(\mathbb{R})\cap
\dot{H}^s(\mathbb{R})$ with $s>3/2$. This paper is essentially self-contained
and does not rely on general results from paradifferential calculus.
