Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
67
Views
3
CrossRef citations to date
0
Altmetric
Articles

Regularity results for deep-water waves with Hölder continuous vorticity

Pages 2144-2151 | Received 16 May 2012, Accepted 31 Jul 2012, Published online: 10 Sep 2012

References

  • Gerstner , F . 1809 . Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile . Ann. Phys. , 2 : 412 – 445 .
  • Constantin , A . 2001 . On the deep water wave motion . J. Phys. A , 34 : 1405 – 1417 .
  • Henry , D . 2008 . On Gerstner's water wave . J. Nonlinear Math. Phys. , 15 : 87 – 95 .
  • Constantin. , A . Nonlinear water waves with applications to wave-current interactions and tsunamis, Volume 81 of CBMS-NSF conference series in applied mathematics. SIAM, Philadelphia, 2011
  • Stuhlmeier , R . 2011 . On edge waves in stratified water along a sloping beach . J. Nonlinear Math. Phys , 18 ( 1 ) : 127 – 137 .
  • Matioc , A-V . An explicit solution for deep water waves with Coriolis effects . J. Nonlinear Math. Phys. , to appear
  • Matioc , B-V and Matioc , A-V . On periodic water waves with Coriolis effects and isobaric streamlines . J. Nonlinear Math. Phys. , to appear
  • Kalisch , H . 2004 . Periodic traveling water waves with isobaric streamlines . J. Nonlinear Math. Phys. , 11 : 461 – 471 .
  • Dubreil-Jacotin , M-L . 1934 . Sur la détermination rigoureuse des ondes permanentes périodiques d'ampleur finite . J. Math. Pures Appl. , 13 : 217 – 291 .
  • Hur , VM . 2006 . Global bifurcation theory of deep-water waves with vorticity . SIAM J. Math. Anal. , 37 ( 5 ) : 1482 – 1521 .
  • Constantin , A and Strauss , W . 2004 . Exact steady periodic water waves with vorticity . Comm. Pure Appl. Math. , 57 ( 4 ) : 481 – 527 .
  • Constantin , A and Escher , J . 2004 . Symmetry of steady deep-water waves with vorticity . Eur. J. Appl. Math. , 15 ( 6 ) : 755 – 768 .
  • Keady , G and Norbury , J . 1978 . On the existence theory for irrotational water waves . Math. Proc. Cambridge Philos. Soc. , 83 : 137 – 157 .
  • Amick , CJ , Fraenkel , LE and Toland , JF . 1982 . On the Stokes conjecture for the wave of extreme form . Acta Math. , 148 : 193 – 214 .
  • Toland , JF . 1996 . Stokes waves . Topol. Methods Nonlinear Anal. , 7 ( 1 ) : 1 – 48 .
  • Henry , D . 2008 . On the deep-water Stokes wave flow . Int. Math. Res. Not. , : 7 Art. ID rnn 071
  • Henry , D . 2011 . Pressure in a deep-water Stokes wave . J. Math. Fluid Mech. , 13 ( 2 ) : 251 – 257 .
  • Constantin , A . 2006 . The trajectories of particles in Stokes waves . Invent. Math. , 166 ( 3 ) : 523 – 535 .
  • Constantin , A and Strauss , W . 2010 . Pressure beneath a Stokes wave . Comm. Pure Appl. Math. , 63 ( 4 ) : 533 – 557 .
  • Lewy , H . 1952 . A note on harmonic functions and a hydrodynamical application . Proc. Am. Math. Soc. , 3 : 111 – 113 .
  • Matioc , B-V . 2012 . On the regularity of deep-water waves with general vorticity distributions . Quart. Appl. Math. , LXX ( 2 ) : 393 – 405 .
  • Constantin , A and Escher , J . 2011 . Analyticity of periodic traveling free surface water waves with vorticity . Ann. Math. , 173 : 559 – 568 .
  • Matioc , B-V . 2011 . Analyticity of the streamlines for periodic traveling water waves with bounded vorticity . Int. Math. Res. Not. , 17 : 3858 – 3871 .
  • Henry , D . 2010 . Analyticity of the streamlines for periodic travelling free surface capillary-gravity water waves with vorticity . SIAM J. Math. Anal , 42 ( 6 ) : 3103 – 3111 .
  • Henry , D . 2012 . Regularity for steady periodic capillary water waves with vorticity . Philos. Trans. R. Soc. London Ser. A , 370 : 1616 – 1628 .
  • Hur , VM . 2011 . Analyticity of rotational flows beneath solitary water waves . Int. Math. Res. Not. , 2012 ( 11 ) : 2550 – 2570 .
  • Matioc , B-V and Matioc , A-V . 2012 . Regularity and symmetry properties of rotational solitary water waves . J. Evol. Equ. , 12 : 481 – 494 .
  • Henry , D and Matioc , B-V . 2012 . On the regularity of steady periodic stratified water waves . Commun. Pure Appl. Anal. , 11 ( 4 ) : 1453 – 1464 .
  • Escher , J . 2012 . Regularity of rotational travelling water waves . Philos. Trans. R. Soc. London Ser. A , 370 : 1602 – 1615 .
  • Li , W-X and Wang , L-J . 2011 . Regularity of traveling free surface water waves with vorticity. , arXiv:1112.2730v1
  • Wang , L-J . 2012 . Regularity of traveling periodic stratified water waves with vorticity. , arXiv:1202.3225v1
  • Constantin , A and Strauss , W . 2011 . Periodic traveling gravity water waves with discontinuous vorticity . Arch. Ration. Mech. Anal. , 202 ( 1 ) : 133 – 175 .
  • Agmon , S , Douglis , A and Nirenberg , L . 1959 . Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I . Comm. Pure Appl. Math. , 12 : 623 – 727 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.