On the two-phase free boundary problem for two-dimensional water waves (Q1380077)

We consider a two-phase free boundary problem for two-dimensional water waves, that is, the irrotational motion of incompressible ideal fluids under the gravitational field, in the case of infinite depth. We establish the well-posedness, locally in time, of this problem in a Sobolev space, taking the surface tension into account. We also remark the case where the surface tension is equal to zero.