Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
131
Views
5
CrossRef citations to date
0
Altmetric
Articles

Temporal boundary value problems in interfacial fluid dynamics

&
Pages 922-948 | Received 01 Sep 2011, Accepted 11 Nov 2011, Published online: 11 Jan 2012

References

  • Duchon , J and Robert , R . 1988 . Global vortex solutions of Euler equations in the plane . J. Differ. Eqns , 73 : 215 – 224 .
  • Valls , C . 2005 . The Boussinesq system: dynamics on the center manifold . Commun. Pure Appl. Anal. , 4 ( 4 ) : 839 – 860 .
  • de la Llave , R . 2009 . A smooth centre manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities . J. Dyn. Differ. Eqns , 21 ( 3 ) : 371 – 415 .
  • Moore , DW . 1979 . The spontaneous appearance of a singularity in the shape of an evolving vortex sheet . Proc. R. Soc. Lond. A. Math. Phys. Sci. , 365 ( 1720 ) : 105 – 119 .
  • Meiron , GR , Baker , DI and Orszag , SA . 1982 . Analytic structure of vortex sheet dynamics. Part 1. Kelvin-Helmholtz instability . J. Fluid Mech. , 114 : 283 – 298 .
  • Krasny , R . 1986 . A study of singularity formation in a vortex sheet by the point-vortex approximation . J. Fluid Mech. , 167 : 65 – 93 .
  • Shelley , MJ . 1992 . A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method . J. Fluid Mech. , 244 : 493 – 526 .
  • Caflisch , RE and Orellana , OF . 1989 . Singular solutions and ill-posedness for the evolution of vortex sheets . SIAM J. Math. Anal. , 20 ( 2 ) : 293 – 307 .
  • Sulem , C , Sulem , PL , Bardos , C and Frisch , U . 1982 . Finite time analyticity for two and three dimensional Kelvin-Helmholtz instability . Commun. Math. Phys. , 80 : 485 – 416 .
  • Wu , S . 2002 . Recent progress in mathematical analysis of vortex sheets , Vol. III, Higher Ed. Press, Beijing : in Proceedings of the International Congress of Mathematicians . pp. 233–242
  • Wu , S . 2006 . Mathematical analysis of vortex sheets . Commun. Pure Appl. Math. , 59 : 1065 – 1206 .
  • Lebeau , G . 2004 . Régularité du probléme de Kelvin-Helmholtz pour l'équation d'Euler 2d . ESAIM Control Optim. Calc. Var. , 8 : 801 – 825 .
  • Kamotski , V and Lebeau , G . 2005 . On 2D Rayleigh-Taylor instabilities . Asymptot. Anal. , 42 : 1 – 27 .
  • Boussinesq , J . 1871 . Théorie de l'intumescence liquide, applelée onde solitaire ou de translation, sepropageant dans un canal rectangulaire . C. R. Acad. Sci. , 72 : 755 – 759 .
  • Boussinesq , J . 1872 . Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond . J. Math. Pures Appl. , 17 : 55 – 108 .
  • Bona , JL , Chen , M and Saut , JC . 2002 . Boussinesq equations and other systems for smallamplitude long waves in nonlinear dispersive media. I: Derivation and linear theory . J. Nonlinear Sci. , 12 : 283 – 318 .
  • Fokas , AS and Pelloni , B . 2002 . Well-posed boundary value problems for integrable evolution equations on a finite interval . Theor. Math. Phys. , 133 : 1598 – 1606 .
  • Fokas , AS and Pelloni , B . 2005 . Boundary value problems for Boussinesq type systems . Math. Phys. Anal. Geom. , 8 : 59 – 96 .
  • Bona , JL , Chen , M and Saut , JC . 2004 . Boussinesq equations and other systems for smallamplitude long waves in nonlinear dispersive media. II: The nonlinear theory . Nonlinearity , 17 : 925 – 952 .
  • Crannell , A . 1996 . The existence of many periodic non-travelling solutions to the Boussinesq equation . J. Differ. Eqns , 126 : 169 – 183 .
  • Ambrose , DM and Wilkening , J . 2010 . Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension . Proc. Natl. Acad. Sci. USA , 107 ( 8 ) : 3361 – 3366 .
  • Ambrose , DM and Wilkening , J . Dependence of time-periodic vortex sheets with surface tension on mean vortex sheet strength, preprint (2011)
  • Lopes Filho , Milton C , Lowengrub , John , Nussenzveig Lopes , Helena J and Zheng , Yuxi . 2006 . Numerical evidence of nonuniqueness in the evolution of vortex sheets . M2AN Math. Model. Numer. Anal. , 40 ( 2 ) : 225 – 237 .
  • Milgrom , T . A study of boundary-value problems in interfacial fluid dynamics, Ph.D. thesis, Drexel University, 2011

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.