Formation of Singularities in Fluid Interfaces

 Access to full text

 Full (PDF)

1. T. Alazard, N. Burq, C. Zuilly, On the water-wave equations with surface tension, Duke Math. J. 158, 413-499 Zbl1258.35043MR2805065
2. D. M. Ambrose, N. Masmoudi, The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math. 58, 1287-1315 Zbl1086.76004MR2162781
3. B. Alvarez-Samaniego, D. Lannes, Large time existence for 3D water waves and asympotics, Invent. Math. 171, 485-541 Zbl1131.76012MR2372806
4. A. Bertozzi, P. Constantin, Global regularity for vortex patches, Comm. Pure Appl. Math. 152, 19-28 Zbl0771.76014MR1207667
5. J. T. Beale, T. Y. Hou, J. Lowengrub, Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal. 33, 1797-1843 Zbl0858.76046MR1411850
6. A. Castro, D. Cordoba, C. Fefferman, F. Gancedo, J. Gomez-Serrano, Finite time singularities for the free boundary incompressible Euler equations Zbl1291.35199
7. A. Castro, D. Cordoba, C. Fefferman, F. Gancedo, J. Gomez-Serrano, Finite time singularities for water waves with surface tension Zbl1328.76012
8. A. Castro, D. Cordoba, C. Fefferman, F. Gancedo, M. Lopez-Fernandez, Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Annals of Math. 175, 909-948 Zbl1267.76033MR2993754
9. A. Castro, D. Cordoba, C. Fefferman, F. Gancedo, Breakdown of smoothness for the Muskat problem 
10. A. Cordoba, D. Cordoba, F. Gancedo, Interface evolution: Water waves in 2D, Adv. Math. 223, 120-173 Zbl1183.35276
11. P. Constantin, D. Cordoba, F. Gancedo, R. Strain, On the global existence for the Muskat problem, JEMS 15, 201-227 Zbl1258.35002MR2998834
12. D. Cordoba, M. Fontelos, A. Mancho, J. L. Rodrigo, Evidence of singularities for a family of contour dynamics equations, Proc. Nat. Acad. Sci. USA 102, 5949-5952 Zbl1135.76315MR2141918
13. D. Cordoba, F. Gancedo, Contour dynamics of incompressible 3D fluids in a porous medium with different densities, Comm. Math. Phys. 273, 445-471 Zbl1120.76064MR2318314
14. J. Y. Chemin, Persistance de structures géometriques dans les fluides incompressibles bidimensionels, Ann. École Norm. Sup. 26, 1-16 Zbl0779.76011MR1235440
15. R. Caflisch, S. Howison, M. Siegel, Global existence, singular solutions and ill-posedness for the Muskat problem, Comm. Pure Appl. Math 57, 1374-1411 Zbl1062.35089MR2070208
16. D. Christodoulou, H. Lindblad, On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53, 1536-1602 Zbl1031.35116MR1780703
17. P. Constantin, M. Pugh, Global solutions for small data to the Hele-Shaw problem, Nonlinearity 6, 393-415 Zbl0808.35104MR1223740
18. D. Coutand, S. Shkoller, On the finite-time splash singularity for the 3D free surface Euler equqations Zbl1285.35071
19. D. Coutand, S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc. 20, 829-930 Zbl1123.35038MR2291920
20. J. Escher, B-V. Matioc, On the parabolicity of the Muskat problem: Well-posedness, fingering and stability results, Z. Annal. Awend 30, 193-218 Zbl1223.35199MR2793001
21. F. Gancedo, Existence for the $\alpha$-patch model and the $QG$ sharp front in Sobolev spaces, Adv. Math. 217, 2569-2598 Zbl1148.35099MR2397460
22. P. Germain, N. Masmoudi, J. Shatah, Global solutions for the gravity water waves equation in dimension 3, Annals of Math. Zbl1241.35003
23. D. Lannes, Well-posedness of the water-waves equation, J. Amer. Math. Soc. 18, 605-654 Zbl1069.35056MR2138139
24. H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, Annals of Math. 162, 109-194 Zbl1095.35021MR2178961
25. J. Rodrigo, On the evolution of sharp fronts for the quasigeostrophic equation, Comm. Pure Appl. Math. 58, 821-866 Zbl1073.35006MR2142632
26. J. Shatah, C. Zeng, Geometry and a-priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math 61, 698-744 Zbl1174.76001MR2388661
27. S. Wu, Almost global well-posedness of the 2D full water wave problem, Invent. Math. 177, 45-135 Zbl1181.35205
28. S. Wu, Global well-posedness of the 3D full water-wave problem, Invent. Math. 184, 125-220 Zbl1221.35304
29. S. Wu, Well-posedness in Sobolev spaces of the full water-wave problem in 2D, Invent. Math. 177, 39-72 Zbl0892.76009MR1471885
30. S. Wu, Well-posedness in Sobolev spaces of the full water-wave problem in 3D, J. Amer. Math. Soc. 12, 445-495 Zbl0921.76017MR1641609
31. F. Yi, Global classical solution of Muskat free boundary problem, J. Math. Anal. Appl. 288, 442-461 Zbl1038.35083MR2019452
32. P. Zhang, Z. Zhang, On the free boundary problem of three-dimensional incompressible Euler equations, Comm. Pure Appl. Math 61, 877-940 Zbl1158.35107MR2410409