[Sur la regularité des ondes progressive périodiques avec vorticité]
Nous étudions la regularité des lignes de courant et des ondes progressive périodiques avec tension superficielle pour le problème d'écoulement rotationnel de l'eau à surface libre.
We study the regularity of the streamlines and of the free-surface in a capillary water flow with underlying currents.
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@article{CRMATH_2011__349_3-4_171_0,
author = {Henry, David},
title = {On the regularity of capillary water waves with vorticity},
journal = {Comptes Rendus. Math\'ematique},
pages = {171--173},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.12.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.12.013/}
}
TY - JOUR AU - Henry, David TI - On the regularity of capillary water waves with vorticity JO - Comptes Rendus. Mathématique PY - 2011 SP - 171 EP - 173 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.12.013/ DO - 10.1016/j.crma.2010.12.013 LA - en ID - CRMATH_2011__349_3-4_171_0 ER -
%0 Journal Article %A Henry, David %T On the regularity of capillary water waves with vorticity %J Comptes Rendus. Mathématique %D 2011 %P 171-173 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.12.013/ %R 10.1016/j.crma.2010.12.013 %G en %F CRMATH_2011__349_3-4_171_0
Henry, David. On the regularity of capillary water waves with vorticity. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 171-173. doi : 10.1016/j.crma.2010.12.013. http://www.numdam.org/articles/10.1016/j.crma.2010.12.013/
[1] Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., Volume 12 (1959), pp. 623-727
[2] Analyticity of periodic travelling free surface water waves with vorticity, Ann. of Math., Volume 172 (2010)
[3] Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., Volume 57 (2004), pp. 481-527
[4] On the regularity of the Neumann problem for the free surfaces with surface tension, Proc. Amer. Math. Soc., Volume 135 (2007), pp. 2497-2504
[5] An exact solution for progressive capillary waves of arbitrary amplitude, J. Fluid Mech., Volume 2 (1957), pp. 532-540
[6] Analyticity of the streamlines for periodic travelling free surface capillary-gravity water waves with vorticity, SIAM J. Math. Anal., Volume 42 (2010) no. 6, pp. 3103-3111
[7] D. Henry, Regularity for steady periodic capillary water waves with vorticity, submited for publication.
[8] H.-C. Hsu, C.-O. Ng, H.-H. Hwung, A new Lagrangian asymptotic solution for gravity-capillary waves in water of finite depth, J. Math. Fluid Mech., available online, , in press. | DOI
[9] Regularity in elliptic free boundary problems, J. Anal. Math., Volume 34 (1978), pp. 86-119
[10] Exact large amplitude capillary waves on sheets of fluid, J. Fluid Mech., Volume 77 (1976), pp. 229-241
[11] Wind Waves, Prentice-Hall, New Jersey, 1965
[12] A note on harmonic functions and a hydrodynamical application, Proc. Amer. Math. Soc., Volume 3 (1952), pp. 111-113
[13] Waves in Fluids, Cambridge University Press, Cambridge, 1978
[14] The Neumann problem for free boundaries in two dimensions, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 597-602
[15] B.V. Matioc, Analyticity of the streamlines for periodic travelling water waves with bounded vorticity, Int. Math. Res. Notices (2010), , in press. | DOI
[16] Steady periodic capillary waves with vorticity, Ark. Mat., Volume 44 (2006), pp. 367-387
[17] S. Walsh, Steady periodic capillary-gravity waves with surface tension, 2009, preprint.
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