Well-posedness of the water-wave problem with surface tension

2008/06/15 by Ming Mei, Mei Ming, Zhifei Zhang +2
Computer Science · Mathematics · #35Q35 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:35Q35

paper · pdf · doi:10.48550/arxiv.0806.2433

32 pages

openalex publication_date 2008/06/15 · arxiv created 2008/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the local well-posedness of the water wave problem with surface tension in the case of finite depth by working in the Eulerian setting. For the flat bottom, as surface tension tends to zero, the solution of the water wave problem with surface tension converges to the solution of the water wave problem without surface tension.

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