On the limit as the surface tension and density ratio tend to zero for the two-phase euler equations

Journal of Hyperbolic Differential Equations

Volumn 8, Issue 2, 2011, Pages 347-373

  Pusateri, Fabio ^a   Masmoudi, N ^b  

^a NEW YORK UNIVERSITY   (United States)

^b NONE

Author keywords

Euler equations; surface tension; vortex sheet problem

Indexed keywords

EID: 79959970992     PISSN: 02198916     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021989161100241X     Document Type: Article

References (21)

1. D. M. Ambrose, Well-posedness of vortex sheets with surface tension, SIAM J. Math. Anal. 35(1) (2003) 211-244.
2. D. M. Ambrose and N. Masmoudi, The zero surface tension limit of two-dimensional water waves, Commun. Pure Appl. Math. 58(9) (2005) 1287-1315. (Pubitemid 41482566)
3. D. M. Ambrose and N. Masmoudi, Well-posedness of 3-d vortex sheets with surface tension, Commun. Math. Sci. 5(2) (2007) 391-430.
4. V. I. Arnold, Sur la ǵeoḿetrie differentielle des groups de Lie de dimension infinie et ses application ̀a l'hydrodynamique des fluids parfait, Ann. Inst. Fourier (Grenoble) 16(1) (1966) 319-361.
5. J. T. Beale, T. Y. Hou and J. S. Lowengrub, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Commun. Pure Appl. Math. 46(9) (1993) 1269-1301.
6. Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Commun. Pure Appl. Math. 52(4) (1999) 411-452.
7. A. Cheng, D. Coutand and S. Shkoller, On the motion of vortex sheets with surface tension, Commun. Pure Appl. Math. 61(12) (2008) 1715-1752.
8. A. Cheng, D. Coutand and S. Shkoller, On the limit as the density ratio tends to zero for two perfect incompressible 3-D fluids separated by a surface of discontinuity, Commun. Partial Differential Equations 35(5) (2010) 817-845.
9. D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Commun. Pure Appl. Math. 53(12) (2000) 1536-1602.
10. D. Coutand and S. Shkoller, Well-posedness of the free surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc. 20(3) (2007) 829-930.
11. G. Ebin, The equations of motion of a perfect fluid with free boundary are not well posed, Commun. Partial Differential Equations 12(10) (1987) 1175-1201.
12. G. Ebin, Ill-posedness of the Raileigh-Taylor and Kelvin-Helmotz problems for incompressible fluids, Commun. Partial Differential Equations 13(10) (1988) 1265-1295.
13. G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math. 92(1) (1970) 102-163.
14. H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, Ann. Math. 162(1) (2005) 109-194. (Pubitemid 43034604)
15. F. Pusateri, On the one fluid limit for vortex sheets, preprint (2009), ArXiv:0908.3353v1.
16. J. Shatah and C. Zeng, Geometry and a priori estimates for Euler's equation, Commun. Pure Appl. Math. 61(5) (2008) 698-744.
17. J. Shatah and C. Zeng, A priori estimates for fluid interface problems, Commun. Pure Appl. Math. 61(6) (2008) 848-876.
18. J. Shatah and C. Zeng, Local well-posedness for the fluid interface problem, preprint (2009).
19. A. Shnirelman, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sb. (N.S.) 128(1) (1985) 82-109, 144.
20. S.Wu,Well-posedness in Sobolev spaces of the full water wave problem in 2-d, Invent. Math. 130(1) (1997) 39-72.
21. S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-d, J. Amer. Math. Soc. 12(2) (1999) 445-495.