Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 2
114
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On free surfaces in hydrostatic flows

Pages 238-245 | Received 23 Jun 2011, Accepted 07 Jul 2011, Published online: 06 Sep 2011

References

  • Renardy , M . 2011 . On hydrostatic free surface problems . J. Math. Fluid Mech. , 13 : 89 – 93 .
  • Renardy , M . 2009 . Ill-posedness of the hydrostatic Euler and NavierStokes equations . Arch. Rational Mech. Anal. , 194 : 877 – 886 .
  • Toland , JF . 1996 . Stokes waves . Topol. Methods Nonlinear Anal. , 7 : 1 – 48 .
  • Constantin , A and Strauss , W . 2004 . Exact steady periodic water waves with vorticity . Comm. Pure Appl. Math. , 57 : 481 – 527 .
  • Constantin , A and Varvaruca , E . 2011 . Steady periodic water waves with constant vorticity: Regularity and local bifurcation . Arch. Rational Mech. Anal. , 199 : 33 – 67 .
  • Wahlén , E . 2009 . Steady water waves with a critical layer . J. Diff. Eqns. , 246 : 2468 – 2483 .
  • Johnson , RS . 1997 . A Modern Introduction to the Mathematical Theory of Water Waves , Cambridge : Cambridge University Press .
  • Lighthill , J . 1978 . Waves in Fluids , Cambridge : Cambridge University Press .
  • Constantin , A and Strauss , W . 2010 . Pressure beneath a Stokes wave . Comm. Pure Appl. Math. , 63 : 533 – 557 .
  • Constantin , A , Escher , J and Hsu , H-C . 2011 . Pressure beneath a solitary water wave: Mathematical theory and experiments . Arch. Rational Mech. Anal. , 201 : 251 – 269 .
  • Escher , J and Schlurmann , T . 2008 . On the recovery of the free surface from the pressure within periodic traveling water waves . J. Nonlinear Math. Phys. , 15 : 50 – 57 .
  • Henry , D . 2011 . Pressure in a deep-water Stokes wave . J. Math. Fluid Mech. , 13 : 251 – 257 .
  • Spielvogel , ER . 1970 . A variational principle for waves of infinite depth . Arch. Rational Mech. Anal. , 39 : 189 – 205 .
  • Varvaruca , E . 2008 . Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth . Proc. Roy. Soc. Edinburgh Sect. A , 138 : 1345 – 1362 .
  • Constantin , A . 2006 . The trajectories of particles in Stokes waves . Invent. Math. , 166 : 523 – 535 .
  • Henry , D . 2006 . The trajectories of particles in deep-water Stokes waves . Int. Math. Res. Not. , 2006 13pp., article ID 23405
  • Henry , D . 2008 . On the deep-water Stokes wave flow . Int. Math. Res. Not. , 2008 7pp., article ID rnn071
  • Fraenkel , LE . 2000 . An Introduction to Maximum Principles and Symmetry in Elliptic Problems , Cambridge : Cambridge University Press .
  • Teles da Silva , AF and Peregrine , DH . 1988 . Steep, steady surface waves on water of finite depth with constant vorticity . J. Fluid Mech. , 195 : 281 – 302 .
  • Constantin , A . 2011 . Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train . Eur. J. Mech. B Fluids , 30 : 12 – 16 .
  • Henry , D . Steady periodic waves bifurcating for fixed-depth rotational flows , preprint
  • Evans , LC . 1998 . “ Partial Differential Equations ” . In American Mathematical Society , Rhode Island : Providence .

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.