On rotational waves of greatest height on water of finite depth
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 107-112.

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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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V. A. Kozlov; E. È. Lokharu. On rotational waves of greatest height on water of finite depth. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 107-112. http://geodesic.mathdoc.fr/item/FAA_2021_55_2_a8/

[1] M. Allen, H. Shahgholian, Arch. Rational Mech. Anal., 234:3 (2019), 1413–1444 | DOI | MR | Zbl

[2] C. J. Amick, L. E. Fraenkel, Trans. Amer. Math. Soc., 299:1 (1987), 273–273 | DOI | MR | Zbl

[3] C. J. Amick, L. E. Fraenkel, J. F. Toland, Acta Math., 148 (1982), 193–214 | DOI | MR | Zbl

[4] C. J. Amick, J. F. Toland, Philos. Trans. Roy. Soc. London Ser. A, 303:1481 (1981), 633–669 | DOI | MR | Zbl

[5] C. J. Amick, J. F. Toland, Arch. Rational Mech. Anal., 76:1 (1981), 9–95 | DOI | MR | Zbl

[6] B. Buffoni, J. Toland, Analytic Theory of Global Bifurcation, Princeton Series Applied Math., Princeton Univ. Press, Princeton, NJ, 2003 | MR | Zbl

[7] A. Constantin, W. Strauss, Comm. Pure Appl. Math., 57:4 (2004), 481–527 | DOI | MR | Zbl

[8] A. Constantin, W. Strauss, Arch. Rational Mech. Anal., 202:1 (2011), 133–175 | DOI | MR | Zbl

[9] A. Constantin, W. Strauss, E. Vărvărucă, Acta Math., 217:2 (2016), 195–262 | DOI | MR | Zbl

[10] M. D. Groves, E. Wahlén, Phys. D: Nonlinear Phenomena, 237:10–12 (2008), 1530–1538 | DOI | MR | Zbl

[11] V. Kozlov, E. Lokharu, arXiv: 2103.14451

[12] V. Kozlov, N. Kuznetsov, E. Lokharu, J. Fluid Mech., 765 (2015), R1 | DOI | MR | Zbl

[13] V. Kozlov, N. Kuznetsov, E. Lokharu, J. Fluid Mech., 825 (2017), 961–1001 | DOI | MR | Zbl

[14] V. Kozlov, E. Lokharu, arXiv: 2010.14156

[15] E. Lokharu, J. Math. Fluid Mech., 2021 (to appear)

[16] J. B. McLeod, Trans. Amer. Math. Soc., 299:1 (1987), 299–299 | DOI | MR | Zbl

[17] J. B. McLeod, Stud. Appl. Math., 98:4 (1997), 311–333 | DOI | MR | Zbl

[18] P. I. Plotnikov, Dinamika sploshnoi sredy, 1982, no. 57, 41–76 | Zbl

[19] P. I. Plotnikov, J. F. Toland, Arch. Rational Mech. Anal., 171:3 (2004), 349–416 | DOI | MR | Zbl

[20] S. W. So, W. A. Strauss, J. Differential Equations, 264:6 (2018), 4136–4151 | DOI | MR | Zbl

[21] G. G. Stokes, Mathematical and Physical Papers, v. 1, Cambridge Univ. Press, Cambridge, 2009, 225–228 | MR

[22] J. F. Toland, Proc. Roy. Soc. London, Ser. A, 363:1715 (1978), 469–485 | DOI | MR | Zbl

[23] K. Varholm, SIAM J. Math. Anal., 52:5 (2020), 5066–5089 | DOI | MR | Zbl

[24] E. Varvaruca, Comm. Partial Differential Equations, 31:10 (2006), 1451–1477 | DOI | MR | Zbl

[25] E. Varvaruca, J. Differential Equations, 246:10 (2009), 4043–4076 | DOI | MR | Zbl

[26] E. Varvaruca, G. S. Weiss, Acta Math., 206:2 (2011), 363–403 | DOI | MR | Zbl

[27] E. Varvaruca, G. S. Weiss, Ann. Inst. H. Poincare (C) Nonlinear Anal., 29:6 (2012), 861–885 | DOI | MR | Zbl

[28] M. H. Wheeler, J. Fluid Mech., 768 (2015), 91–112 | DOI | MR | Zbl