  In this paper we establish the well-posedness of the Muskat problem with
surface tension and equal viscosities in the subcritical Sobolev spaces
$W^s_p(\mathbb{R})$, where ${p\in(1,2]}$ and ${s\in(1+1/p,2)}$. This is
achieved by showing that the mathematical model can be formulated as a
quasilinear parabolic evolution problem in $W^{\overline{s}-2}_p(\mathbb{R})$,
where ${\overline{s}\in(1+1/p,s)}$. Moreover, we prove that the solutions
become instantly smooth and we provide a criterion for the global existence of
solutions.
