Zero surface tension limit of viscous surface waves
Analysis of PDEs
2015-10-07 v1
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.
Cite
@article{arxiv.1212.1017,
title = {Zero surface tension limit of viscous surface waves},
author = {Zhong Tan and Yanjin Wang},
journal= {arXiv preprint arXiv:1212.1017},
year = {2015}
}
Comments
57pp. arXiv admin note: substantial text overlap with arXiv:1011.5179, arXiv:1109.1798