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Zero Surface Tension Limit of Viscous Surface Waves

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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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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China

    Zhong Tan & Yanjin Wang

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  1. Zhong Tan
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  2. Yanjin Wang
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Correspondence to Yanjin Wang.

Additional information

Communicated by L. Caffarelli

Y. J. Wang was supported by the National Natural Science Foundation of China (No. 11201389), the Natural Science Foundation of Fujian Province of China (No. 2012J05011), the Specialized Research Fund for the Doctoral program of Higher Education (No. 20120121120023), and the Fundamental Research Funds for the Central Universities (No. 2013121002). Z. Tan was supported by the National Natural Science Foundation of China (No. 11271305).

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Tan, Z., Wang, Y. Zero Surface Tension Limit of Viscous Surface Waves. Commun. Math. Phys. 328, 733–807 (2014). https://doi.org/10.1007/s00220-014-1986-0

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  • DOI: https://doi.org/10.1007/s00220-014-1986-0

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