We study the regularity of the streamlines and of the free-surface in a capillary water flow with underlying currents.
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.
Accepted:
Published online:
David Henry 1
@article{CRMATH_2011__349_3-4_171_0, author = {David Henry}, 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}, }
David Henry. On the regularity of capillary water waves with vorticity. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 171-173. doi : 10.1016/j.crma.2010.12.013. https://comptes-rendus.academie-sciences.fr/mathematique/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.
Cited by Sources:
Comments - Policy