Finite time singularities for water waves with surface tension

Journal of Mathematical Physics

Volumn 53, Issue 11, 2012, Pages

  Castro, Angel ^a   Córdoba, Diego ^b   Fefferman, Charles ^c   Gancedo, Francisco ^d   Gómez Serrano, Javier ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b CSIC   (Spain)

^c PRINCETON UNIVERSITY   (United States)

^d UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84870547349     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4765339     Document Type: Article

References (28)

1. Alazard T. Burq N. Zuily C. On the water-wave equations with surface tension. Duke Math. J. 2011, 158(3):413-499. 10.1215/00127094-1345653
2. Alazard T. Métivier G. Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Commun. Partial Differ. Equ. 2009, 34(10-12):1632-1704. 10.1080/03605300903296736
3. Alvarez-Samaniego B. Lannes D. Large time existence for 3D water-waves and asymptotics. Invent. Math. 2008, 171(3):485-541. 10.1007/s00222-007-0088-4
4. Ambrose D.M. Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 2003, 35(1):211-244. 10.1137/S0036141002403869.
5. Ambrose D.M. Masmoudi N. The zero surface tension limit of two-dimensional water waves. Commun. Pure Appl. Math. 2005, 58(10):1287-1315. 10.1002/cpa.20085
6. Ambrose D.M. Masmoudi N. The zero surface tension limit of three-dimensional water waves. Indiana Univ. Math. J. 2009, 58(2):479-521. 10.1512/iumj.2009.58.3450
7. Beale J.T. Hou T.Y. Lowengrub J.S. Growth rates for the linearized motion of fluid interfaces away from equilibrium. Commun. Pure Appl. Math. 1993, 46(9):1269-1301. 10.1002/cpa.3160460903
8. Castro A. Córdoba D. Fefferman C. Gancedo F. Gómez-Serrano J. Finite time singularities for the free boundary incompressible Euler equations. 2011, and e-print arXiv:1112.2170.
9. Castro A. Córdoba D. Fefferman C. Gancedo F. Gómez-Serrano J. Splash singularity for water waves. Proc. Natl. Acad. Sci. U.S.A. 2012, 109(3):733-738. 10.1073/pnas.1115948108
10. Castro A. Córdoba D. Fefferman C. Gancedo F. López-Fernández M. Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves. Ann. Math. 2012, 175(2):909-948. 10.4007/annals.2012.175.2.9
11. Christodoulou D. Lindblad H. On the motion of the free surface of a liquid. Commun. Pure Appl. Math. 2000, 53(12):1536-1602. 10.1002/1097-0312(200012)53:12<1536::AID-CPA23.0.CO;2-Q
12. Córdoba A. Córdoba D. Gancedo F. Interface evolution: water waves in 2-D. Adv. Math. 2010, 223(1):120-173. 10.1016/j.aim.2009.07.016
13. Coutand D. Shkoller S. Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Am. Math. Soc. 2007, 20(3):829-930. 10.1090/S0894-0347-07-00556-5
14. Coutand D. Shkoller S. On the finite-time splash and splat singularities for the 3-D free-surface Euler equations. and e-print arXiv:1201.4919 (2012).
15. Craig W. An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Commun. Partial Differ. Equ. 1985, 10(8):787-1003. 10.1080/03605308508820396.
16. Germain P. Masmoudi N. Shatah J. Global solutions for the gravity water waves equation in dimension 3. Ann. Math. 2012, 175(2):691-754. 10.4007/annals.2012.175.2.6
17. Hou T.Y. Lowengrub J.S. Shelley M.J. Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 1994, 114(2):312-338. 10.1006/jcph.1994.1170
18. Lannes D. Well-posedness of the water-waves equations. J. Am. Math. Soc. 2005, 18(3):605-654. 10.1090/S0894-0347-05-00484-4.
19. Lannes D. A stability criterion for two-fluid interfaces and applications. 2010, e-print arXiv:1005.4565.
20. Lindblad H. Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. Math. 2005, 162(1):109-194. 10.4007/annals.2005.162.109.
21. Nalimov V.I. The Cauchy-Poisson problem. 1974, 104-210. Dinamika Splon. Sredy (Vyp. 18 Dinamika Zidkost. so Svobod. Granicami) pp.
22. Shatah J. Zeng C. Geometry and a priori estimates for free boundary problems of the Euler equation. Commun. Pure Appl. Math. 2008, 61(5):698-744. 10.1002/cpa.20213
23. Wu S. Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 1997, 130(1):39-72. 10.1007/s002220050177.
24. Wu S. Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 1999, 12(2):445-495. 10.1090/S0894-0347-99-00290-8.
25. Wu S. Almost global wellposedness of the 2-D full water wave problem. Invent. Math. 2009, 177(1):45-135. 10.1007/s00222-009-0176-8.
26. Wu S. Global wellposedness of the 3-D full water wave problem. Invent. Math. 2011, 184(1):125-220. 10.1007/s00222-010-0288-1.
27. Yosihara H. Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. Res. Inst. Math. Sci. 1982, 18(1):49-96. 10.2977/prims/1195184016.
28. Zhang P. Zhang Z. On the free boundary problem of three-dimensional incompressible Euler equations. Commun. Pure Appl. Math. 2008, 61(7):877-940. 10.1002/cpa.20226