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Zbl 1120.35078
Iguchi, Tatsuo
A mathematical justification of the forced Korteweg-de Vries equation for capillary-gravity waves. (English)
[J] Kyushu J. Math. 60, No. 2, 267-303 (2006). ISSN 1340-6116

Paper deals with a 2D irrotational flow of an incompressible ideal fluid with a free surface under the gravitational field. The domain occupied by the fluid is bounded from below by a solid bottom and above by an atmosphere of constant pressure. Mathematically, the problem is formulated as a free boundary problem for the incompressible Euler equation with the irrotational conditions. Author formally derives the forced KdV equation as a long-wave approximation and proves existence under some natural assumptions existence of the unique solution.
[Igor Andrianov (Köln)]

MSC 2000:: *35Q53 KdV-like equations
76B15 Wave motions (fluid mechanics)
76B45 Capillarity
35Q35 Other equations arising in fluid mechanics

Keywords: capillary-gravity waves; forced KdV equation; long-wave approximation

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