Email this article Unique solvability of the water waves problem in Sobolev spaces
- Authors: Nalimov V.I.1
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Affiliations:
- Lavrent’ev Institute of Hydrodynamics
- Issue: Vol 57, No 1 (2016)
- Pages: 97-123
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170333
- DOI: https://doi.org/10.1134/S0037446616010110
- ID: 170333
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Abstract
Studying the problem of unsteady waves on the surface of an infinitely deep heavy incompressible ideal fluid, we derive equations for the height of the free surface as well as the vertical and horizontal components of velocity on the free surface. We prove that the initial-boundary value water waves problem is short-time solvable in Sobolev spaces.
About the authors
V. I. Nalimov
Lavrent’ev Institute of Hydrodynamics
Author for correspondence.
Email: smj@math.nsc.ru
Russian Federation, Novosibirsk
