On the regularity of capillary water waves with vorticity;Sur la regularité des ondes progressive périodiques avec vorticité

Comptes Rendus Mathematique

Volumn 349, Issue 3-4, 2011, Pages 171-173

  Henry, David ^a  

^a DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551496267     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2010.12.013     Document Type: Article

References (17)

1. Agmon S., Douglis A., Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math. 1959, 12:623-727.
2. Constantin A., Escher J. Analyticity of periodic travelling free surface water waves with vorticity. Ann. of Math. 2010, 172.
3. Constantin A., Strauss W. Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math. 2004, 57:481-527.
4. Craig W., Matei A.-M. On the regularity of the Neumann problem for the free surfaces with surface tension. Proc. Amer. Math. Soc. 2007, 135:2497-2504.
5. Crapper G.D. An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 1957, 2:532-540.
6. Henry D. Analyticity of the streamlines for periodic travelling free surface capillary-gravity water waves with vorticity. SIAM J. Math. Anal. 2010, 42(6):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:10.1007/s00021-010-0045-7.
9. Kinderlehrer D., Nirenberg L., Spruck J. Regularity in elliptic free boundary problems. J. Anal. Math. 1978, 34:86-119.
10. Kinnersley W. Exact large amplitude capillary waves on sheets of fluid. J. Fluid Mech. 1976, 77:229-241.
11. Kinsman B. Wind Waves 1965, Prentice-Hall, New Jersey.
12. Lewy H. A note on harmonic functions and a hydrodynamical application. Proc. Amer. Math. Soc. 1952, 3:111-113.
13. Lighthill J. Waves in Fluids 1978, Cambridge University Press, Cambridge.
14. Matei A.-M. The Neumann problem for free boundaries in two dimensions. C. R. Acad. Sci. Paris, Ser. I 2002, 335:597-602.
15. B.V. Matioc, Analyticity of the streamlines for periodic travelling water waves with bounded vorticity, Int. Math. Res. Notices (2010), in press. doi:10.1093/imrn/rnq235.
16. Wahlén E. Steady periodic capillary waves with vorticity. Ark. Mat. 2006, 44:367-387.
17. S. Walsh, Steady periodic capillary-gravity waves with surface tension, 2009, preprint.