Regularization of the Kelvin-Helmholtz instability by surface tension

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 365, Issue 1858, 2007, Pages 2253-2266

  Ambrose, David M ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Kelvin Helmholtz instability; Vortex sheet; Well posedness

Indexed keywords

EID: 34548285975     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2007.2006     Document Type: Article

References (23)

1. Ambrose, D. M. 2003 Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 35, 211-244. (doi:10.1137/S0036141002403869)
2. Ambrose, D. M. & Masmoudi, N. In press. Well-posedness of 3D vortex sheets with surface tension. Quart. Appl. Math.
3. Baker, G., Meiron, D. & Orszag, S. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501. (doi:10.1017/S0022112082003164)
4. Beale, J. T., Hou, T. Y. & Lowengrub, J. S. 1993 Growth rates for the linearized motion of fluid interfaces away from equilibrium, Comm. Pure Appl. Math. 46, 1269-1301.
5. Caflisch, R. E. & Li, X.-F. 1992 Lagrangian theory for 3D vortex sheets with axial or helical symmetry. Transport Theory Stat. Phys. 21, 559-578.
6. Caflisch, R. &: Orellana, O. F. 1986 Long time existence for a slightly perturbed vortex sheet. Comm. Pure Appl. Math. 36, 807-838.
7. Coutand, D. & Shkoller, S. In press. Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Amer. Math. Soc.
8. Delort, J.-M. 1991 Existence de nappes de tourbillon en dimension deux. J. Am. Math. Soc. 4, 553-586. (doi: 10.2307/2939269)
9. Evans, L. C. & Müller, S. 1994 Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity. J. Am. Math. Soc. 7, 199-219. (doi:10.2307/2152727)
10. Guo, Y., Hallstrom, C. & Spirn, D. In press. Dynamics near unstable interfacial fluids. Commun. Math. Phys.
11. Hou, T. & Hu, G. 2003 A nearly optimal existence result for slightly perturbed 3D vortex sheets. Comm. Partial Differ. Equations 28, 155-198. (doi:10.1081/PDE-120019378)
12. Hou, T., Lowengrub, J. & Shelley, M. 1994 Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114, 312-338. (doi:10.1006/jcph.l994.1170)
13. Hou, T., Lowengrub, J. & Shelley, M. 1997 The long-time motion of vortex sheets with surface tension. Phys. Fluids 9, 1933-1954. (doi:10.1063/1.869313)
14. Larmes, D. 2005 Well-posedness of the water-waves equations. J. Am. Math. Soc. 18, 605-654. (doi: 10.1090/S0894-0347-05-00484-4)
15. Lebeau, G. 2002 Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d. ESAIM Control Optim. Cale. Var. 8, 801 825. (doi:10.1051/cocv:2002052)
16. Lindblad, H. 2005 Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. Math. 162, 109-194.
17. Lopes Filho, M. C., Nussenzveig Lopes, H. J. & Xin, Z. 2001 Existence of vortex sheets with reflection symmetry in two space dimensions. Arch. Ration. Mech. Anal. 158, 235-257. (doi:10. 1007/S002050100145)
18. Majda, A. J. 1993 Remarks on weak solutions for vortex sheets with a distinguished sign. Ind. Univ. Math. J. 42, 921-939. (doi:10.1512/iumj.1993.42.42043)
19. Saffman, P. G. 1995 Vortex dynamics. Cambridge, UK: Cambridge University Press.
20. Schochet, S. 1995 The weak vorticity formulation of the 2-D Euler equations and concentration-cancellation. Comm. Partial Differ. Equations 20, 1077-1104.
21. Wu, S. 1997 Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130, 39-72. (doi:10.1007/ s002220050177)
22. Wu, S. 1999 Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 12, 445-495. (doi:10.1090/S0894-0347-99-00290-8)
23. Wu, S. 2006 Mathematical analysis of vortex sheets. Comm. Pure Appl. Math. 59, 1065-1206. (doi:10.1002/cpa.20110)