On the two-phase free boundary problem for two-dimensional water waves. (English) Zbl 0897.76017
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.
Reviewer: T.Iguchi, N.Tanaka, A.Tani (Tokyo)
MSC:
76B55 | Internal waves for incompressible inviscid fluids |
76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
35Q35 | PDEs in connection with fluid mechanics |
76V05 | Reaction effects in flows |
76B45 | Capillarity (surface tension) for incompressible inviscid fluids |