A nearly optimal existence result for slightly perturbed 3-D vortex sheets

Communications in Partial Differential Equations

Volumn 28, Issue 1-2, 2003, Pages 155-198

  Hou, Thomas Y ^a   Hu, Gang ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

3 D vortex sheets; Existence theory; Kelvin Helmholtz instability

Indexed keywords

EID: 0038473867     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-120019378     Document Type: Article

References (25)

1. Ahlfors LV. Complex analysis. New York: McGraw-Hill, Inc. 1966.
2. Baker GR. Generalized vortex methods for free-surface flows, In: Waves on Fluid Interfaces, ed. Meyer RE. New York: Academic Press 1983:53-81.
3. Batchelor GK. An Introduction to fluid dynamics. Cambridge: Cambridge University Press. 1970.
4. Birkhoff G. Helmholtz and Taylor instability. Proc Symp Appl Math Am Math Soc 1962; 13:55-76.
5. Brady M, Pullin DI. On singularity formation in three-dimensional vortex sheet evolution. Phys Fluids 1999; 11(11):3198-3200.
6. Caflisch RE. Li X. Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry. Transport Th and Stat Phys 1992; 21:559-578.
7. Caflisch RE. Orellana OF. Long time existence for a slightly perturbed vortex sheet. Comm Pure Appl Math 1986; 39:1-18.
8. Caflisch RE. Orellana OF. Singular solutions and Ill-posedness for the evolution of vortex sheets. SIAM J Math Anal 1989; 20:293-307.
9. Calderón AP. Zygmund A. Singular integrals and periodic functions. Studia Math 1954; 14:249-271.
10. Cowley SJ. Baker GR. Tanveer S. On the formation of moore-curvature singularities in vortex sheets. J Fluid Mech 1999;378:233-267.
11. Duchon J. Roberts R. Global vortex sheet solutions of euler equations in the plane. J Differ Equations 1988; 73(2):215-224.
12. Haroldsen DJ. Meiron DI. Numerical calculation of three-dimensional interfacial potential flows using the point vortex method. SIAM J Sci Comput 1998; 20(2):648-683.
13. Hou TY. Teng ZH. Zhang P. Well-posedness of linearized motion for 3-D water waves far from equilibrium. Commun. in Partial Differential Equations 1996; 21(10):1551-1585.
14. Hou TY. Zhang P. Growth rates for the linearized motion of 3-D fluid interfaces with surface tension far from equilibrium. Asian J Math 1998; 2(2):263-288.
15. Hou TY. Hu G. Zhang P. Singularity formation in 3-D vortex sheets, Physics of Fluids 2003; 15(1):147-172.
16. Ishihara T. Kaneda Y. Singularity formation in three-dimensional motion of a vortex sheet. J Fluid Mech 1994; 300:339-366.
17. Krasny RA Study of singularity formation in a vortex sheet by the point vortex method. J Fluid Mech 1986; 167:65-93.
18. Meiron DI. Baker GR. Orzsag SA. Analytic structure of vortex-sheet dynamics. Part 1. Kelvin-Helmholtz Instability. J Fluid Mech 1982; 114:283-298.
19. Moore DW. The Spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc R Soc Lond 1979; A365:105-119.
20. Nishida TA. Note on a theorem of nirenberg. J Diff Geom 1977; 12:629-633.
21. Saffman PG. Baker GR. Vortex interactions. Ann Rev Fluid Mech 1979; 11:95-122.
22. Shelley MJ. A Study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method. J Fluid Mech 1992; 244:493-526.
23. Stein EM. Singular integrals and differentiability properties of functions. Princeton: Princeton University Press, 1970.
24. Sulem C. Sulem PL. Bardos C. Frisch U. Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability. Commun. Math Phys 1981; 80:485-516.
25. Taibleson MH. The preservation of lipschitz spaces under singular integral operators. Studia Math 1963; 24:105-111.