Existence and amplitude bounds for irrotational water waves in finite depth
2017 ◽
Vol 376
(2111)
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pp. 20170094
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We prove the existence of solutions to the irrotational water-wave problem in finite depth and derive an explicit upper bound on the amplitude of the nonlinear solutions in terms of the wavenumber, the total hydraulic head, the wave speed and the relative mass flux. Our approach relies upon a reformulation of the water-wave problem as a one-dimensional pseudo-differential equation and the Newton–Kantorovich iteration for Banach spaces. This article is part of the theme issue ‘Nonlinear water waves’.
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1971 ◽
Vol 49
(1)
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pp. 65-74
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2010 ◽
Vol 106
(1)
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pp. 141
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1997 ◽
Vol 342
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pp. 199-229
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2001 ◽
Vol 439
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pp. 255-278
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1979 ◽
Vol 17
(5)
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pp. 527-532
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2010 ◽
Vol 651
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pp. 211-239
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1973 ◽
Vol 11
(10)
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pp. 1121-1130
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2012 ◽
Vol 370
(1964)
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pp. 1602-1615
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