Large-time regularity of viscous surface waves. (English) Zbl 0545.76029

The incompressible fluid which obeys Navier-Stokes equations is subject to surface tension on its upper boundary. It is shown that singularities cannot develop in flows of sufficiently small amplitudes. A unique solution exists for all times in a space defined by Sobolev norms provided the initial state is close to equilibrium.
Reviewer: G.Boillat


76D05 Navier-Stokes equations for incompressible viscous fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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