Zero Surface Tension Limit of Viscous Surface Waves |
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Authors: | Zhong Tan Yanjin Wang |
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Institution: | 1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China
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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. |
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