Non-existence of three-dimensional travelling water waves with constant non-zero vorticity
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AbstractWe prove that there are no three-dimensional bounded travelling gravity waves with constant non-zero vorticity on water of finite depth. The result also holds for gravity–capillary waves under a certain condition on the pressure at the surface, which is satisfied by sufficiently small waves. The proof relies on unique continuation arguments and Liouville-type results for elliptic equations.
1987 ◽
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1994 ◽
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1986 ◽
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1976 ◽
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