An alternative approach to study irrotational periodic gravity water waves
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AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.
2012 ◽
Vol 370
(1964)
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pp. 1602-1615
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1971 ◽
Vol 49
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pp. 65-74
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2004 ◽
Vol 332
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pp. 73-78
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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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1996 ◽
Vol 315
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pp. 257-266
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2010 ◽
Vol 651
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pp. 211-239
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1967 ◽
Vol 27
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pp. 395-397
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2017 ◽
Vol 376
(2111)
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pp. 20170094
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