  Regularizing effects of surface tension are studied for interfacial waves
between a two-dimensional, infinitely-deep and irrotational flow of water and
vacuum. The water wave problem under the influence of surface tension is
formulated as a system of second-order in time nonlinear dispersive equations.
The main result states that if the curvature of the initial fluid surface is in
the Sobolev space of order k+7/2 and if its derivatives decay faster than a
polynomial of degree k+1 does then the curvature of the fluid surface
corresponding to the solution of the problem instantaneously gains k/2
derivatives of smoothness compared to the initial state. The proof uses energy
estimates under invariant vector fields of the associated linear operator.
