Zero surface tension limit of viscous surface waves

Abstract

We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the "semi-small" initial data, we prove the zero surface tension limit of the problem within a local time interval. The unique local strong solution with surface tension is constructed as the limit of a sequence of approximate solutions to a special parabolic regularization. For the small initial data, we prove the global-in-time zero surface tension limit of the problem.

57pp. arXiv admin note: substantial text overlap with arXiv:1011.5179, arXiv:1109.1798

References in corpus (1)

• On the interaction between quasilinear elastodynamics and the Navier-Stokes equations

Cited by in corpus (2)

• The compressible viscous surface-internal wave problem: stability and vanishing surface tension limit
• Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension