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On Rotational Waves of Limit Amplitude

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Abstract

In this note we discuss some recent results on extreme steady waves under gravity. They include the existence and regularity theorems for highest waves on finite depth with and without vorticity. Furthermore, we state new results concerning the asymptotic behavior of surface profiles near stagnation points. In particular, we find that the wave profile of an extreme wave is concave near each crest, provided that the vorticity is negative near the surface.

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Funding

V. K. was supported by the Swedish Research Council (VR), 2017-03837.

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Correspondence to V. A. Kozlov or E. E. Lokharu.

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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 107–112 https://doi.org/10.4213/faa3862.

In memoriam of M. Z. Solomyak

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Kozlov, V.A., Lokharu, E.E. On Rotational Waves of Limit Amplitude. Funct Anal Its Appl 55, 165–169 (2021). https://doi.org/10.1134/S0016266321020088

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  • DOI: https://doi.org/10.1134/S0016266321020088

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