A remark on the two dimensional water wave problem with surface tension

Shuanglin Shao, Hsi-Wei Shih

Research output: Contribution to journalArticle

Abstract

We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into an equivalent quasilinear system which is related to the interface's tangent angle and a quantity related to the difference of tangential velocities of the interface in the Lagrangian and the arc-length coordinates. The new way is relatively simple because it involves only taking differentiation and the real and the imaginary parts. Then if assuming that waves are periodic, we establish a priori energy inequality.

Original languageEnglish
Pages (from-to)5748-5771
Number of pages24
JournalJournal of Differential Equations
Volume266
Issue number9
DOIs
Publication statusPublished - 2019 Apr 15

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Water waves
Water Waves
Surface Tension
Surface tension
Air
Energy Inequality
Water
Quasilinear System
Arc length
Tangent line
Angle
Motion

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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A remark on the two dimensional water wave problem with surface tension. / Shao, Shuanglin; Shih, Hsi-Wei.

In: Journal of Differential Equations, Vol. 266, No. 9, 15.04.2019, p. 5748-5771.

Research output: Contribution to journalArticle

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