Turning waves and breakdown for incompressible flows

Proceedings of the National Academy of Sciences of the United States of America

Volumn 108, Issue 12, 2011, Pages 4754-4759

  Castro, Angel ^a   Córdoba, Diego ^a   Fefferman, Charles L ^b   Gancedo, Francisco ^c   López Fernández, María ^d  

^a INSTITUTO DE CIENCIAS MATEMÁTICAS   (Spain)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSITY OF CHICAGO   (United States)

^d UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPRESSION; COMPUTATIONAL FLUID DYNAMICS; EVOLUTION; FLUID FLOW; INTERFACE PRESSURE; PRIORITY JOURNAL; WATER ANALYSIS; WAVEFORM;

EID: 79953190074     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1101518108     Document Type: Article

References (26)

1. Muskat M (1934) Two fluid systems in porous media. The encroachment of water into an oil sand. Physics 5:250-264.
2. Saffman P-G, Taylor G (1958) The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc R Soc London Ser A 245:312-329.
3. Howison S (2000) A note on the two-phase Hele-Shaw problem. J Fluid Mech 409:243-249.
4. Hele-Shaw HS (1898) On the motion of a viscous fluid between two parallel plates. Trans Royal Inst Nav Archit, London 40:21.
5. Bardos C, Lannes D (2010) Mathematics for 2D interfaces. ArXiv:1005.5329.
6. Rayleigh J-W-S (1878) On the instability of jets. Proc Lond Math Soc 10:4-13.
7. Siegel M, Caflisch R, Howison S (2004) Global existence, singular solutions, and ill-posedness for the muskat problem. Commun Pur Appl Math 57:1374-1411. (Pubitemid 39234321)
8. Yi F (1996) Local classical solution of Muskat free boundary problem. J Partial Diff Eqs 9:84-96.
9. Córdoba A, Córdoba D, Gancedo F (2011) Interface evolution: The Hele-Shaw and Muskat problems. Ann Math 173:477-542.
10. Ambrose D (2004) Well-posedness of two-phase Hele-Shaw flow without surface tension. Eur J Appl Math 15:597-607.
11. Córdoba D, Gancedo F (2007) Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Commun Math Phys 273:445-471.
12. Constantin P, Pugh M (1993) Global solutions for small data to the Hele-Shaw problem. Nonlinearity 6:393-415.
13. Yi F (2003) Global classical solution of Muskat free boundary problem. J Math Anal Appl 288:442-461.
14. Escher J, Matioc B-V (2010) On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results. ArXiv:1005.2512.
15. Córdoba D, Gancedo F (2009) A maximum principle for the Muskat problem for fluids with different densities. Comm Math Phys 286:681-696.
16. Constantin P, Córdoba D, Gancedo F, Strain R-M (2010) On the global existence for the for the Muskat problem. ArXiv:1007.3744v1.
17. Córdoba D, Gancedo F, Orive R (2008) A note on the interface dynamics for convection in porous media. Physica D 237:1488-1497.
18. Córdoba A, Córdoba D, Gancedo F (2010) Interface evolution: Water wave in 2D. Adv Math 223:120-173.
19. Wu S (1997) Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent math 130:39-72.
20. Lannes D (2005) Well-posedness of the water-waves equations. J Am Math Soc 18:605-654.
21. Wu S (2009) Almost global wellposedness of the 2-D full water wave problem. Invent Math 177:45135.
22. Germain P, Masmoudi N, Shatah J (2009) Global solutions for the gravity water waves equation in dimension 3. C R Math Acad Sci 347:897-902.
23. Wu S (2009) Global well-posedness of the 3-D full water wave problem. ArXiv:0910.2473.
24. Nirenberg L (1972) An abstract form of the nonlinear Cauchy-Kowalewski theorem. J Differ Geom 6:561-576.
25. Nishida T (1977) A note on a theorem of Nirenberg. J Differ Geom 12:629-633.
26. Sulem C, Sulem P-L, Bardos C, Frisch U (1981) Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability. Commun Math Phys 80:485-516.