Formation of Singularities in Fluid Interfaces
Journées équations aux dérivées partielles (2012), article no. 2, 9 p. 
@article{JEDP_2012____A2_0,
     author = {Charles Fefferman},
     title = {Formation of {Singularities} in {Fluid} {Interfaces}},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2012},
     doi = {10.5802/jedp.85},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.85/}
}
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Charles Fefferman. Formation of Singularities in Fluid Interfaces. Journées équations aux dérivées partielles (2012), article  no. 2, 9 p. doi : 10.5802/jedp.85. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.85/

[1] T. Alazard; N. Burq; C. Zuilly On the water-wave equations with surface tension, Duke Math. J., Volume 158 no. 3, pp. 413-499 | MR | Zbl

[2] D. M. Ambrose; N. Masmoudi The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math., Volume 58 no. 10, pp. 1287-1315 | MR | Zbl

[3] B. Alvarez-Samaniego; D. Lannes Large time existence for 3D water waves and asympotics, Invent. Math., Volume 171 no. 3, pp. 485-541 | MR | Zbl

[4] A. Bertozzi; P. Constantin Global regularity for vortex patches, Comm. Pure Appl. Math., Volume 152 no. 1, pp. 19-28 | MR | Zbl

[5] J. T. Beale; T. Y. Hou; J. Lowengrub Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal., Volume 33 no. 5, pp. 1797-1843 | MR | Zbl

[6] A. Castro; D. Cordoba; C. Fefferman; F. Gancedo; J. Gomez-Serrano Finite time singularities for the free boundary incompressible Euler equations (preprint)

[7] A. Castro; D. Cordoba; C. Fefferman; F. Gancedo; J. Gomez-Serrano Finite time singularities for water waves with surface tension (preprint)

[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., Volume 175, pp. 909-948 | MR | Zbl

[9] A. Castro; D. Cordoba; C. Fefferman; F. Gancedo Breakdown of smoothness for the Muskat problem (preprint)

[10] A. Cordoba; D. Cordoba; F. Gancedo Interface evolution: Water waves in 2D, Adv. Math., Volume 223 no. 1, pp. 120-173 | Zbl

[11] P. Constantin; D. Cordoba; F. Gancedo; R. Strain On the global existence for the Muskat problem, JEMS, Volume 15 no. 1, pp. 201-227 | DOI | EuDML | MR | Zbl

[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, Volume 102, pp. 5949-5952 | MR | Zbl

[13] D. Cordoba; F. Gancedo Contour dynamics of incompressible 3D fluids in a porous medium with different densities, Comm. Math. Phys., Volume 273 no. 2, pp. 445-471 | MR | Zbl

[14] J. Y. Chemin Persistance de structures géometriques dans les fluides incompressibles bidimensionels, Ann. École Norm. Sup., Volume 26, pp. 1-16 | Numdam | MR | Zbl

[15] R. Caflisch; S. Howison; M. Siegel Global existence, singular solutions and ill-posedness for the Muskat problem, Comm. Pure Appl. Math, Volume 57, pp. 1374-1411 | MR | Zbl

[16] D. Christodoulou; H. Lindblad On the motion of the free surface of a liquid, Comm. Pure Appl. Math., Volume 53 no. 12, pp. 1536-1602 | MR | Zbl

[17] P. Constantin; M. Pugh Global solutions for small data to the Hele-Shaw problem, Nonlinearity, Volume 6, pp. 393-415 | MR | Zbl

[18] D. Coutand; S. Shkoller On the finite-time splash singularity for the 3D free surface Euler equqations (preprint)

[19] D. Coutand; S. Shkoller Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc., Volume 20 no. 3, pp. 829-930 | MR | Zbl

[20] J. Escher; B-V. Matioc On the parabolicity of the Muskat problem: Well-posedness, fingering and stability results, Z. Annal. Awend, Volume 30, pp. 193-218 | MR | Zbl

[21] F. Gancedo Existence for the α-patch model and the QG sharp front in Sobolev spaces, Adv. Math., Volume 217, pp. 2569-2598 | MR | Zbl

[22] P. Germain; N. Masmoudi; J. Shatah Global solutions for the gravity water waves equation in dimension 3, Annals of Math. | Zbl

[23] D. Lannes Well-posedness of the water-waves equation, J. Amer. Math. Soc., Volume 18 no. 3, pp. 605-654 | MR | Zbl

[24] H. Lindblad Well-posedness for the motion of an incompressible liquid with free surface boundary, Annals of Math., Volume 162, pp. 109-194 | MR | Zbl

[25] J. Rodrigo On the evolution of sharp fronts for the quasigeostrophic equation, Comm. Pure Appl. Math., Volume 58 no. 6, pp. 821-866 | MR | Zbl

[26] J. Shatah; C. Zeng Geometry and a-priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math, Volume 61 no. 5, pp. 698-744 | MR | Zbl

[27] S. Wu Almost global well-posedness of the 2D full water wave problem, Invent. Math., Volume 177 no. 1, pp. 45-135 | Zbl

[28] S. Wu Global well-posedness of the 3D full water-wave problem, Invent. Math., Volume 184 no. 1, pp. 125-220 | Zbl

[29] S. Wu Well-posedness in Sobolev spaces of the full water-wave problem in 2D, Invent. Math., Volume 177, pp. 39-72 | MR | Zbl

[30] S. Wu Well-posedness in Sobolev spaces of the full water-wave problem in 3D, J. Amer. Math. Soc., Volume 12 no. 2, pp. 445-495 | MR | Zbl

[31] F. Yi Global classical solution of Muskat free boundary problem, J. Math. Anal. Appl., Volume 288, pp. 442-461 | MR | Zbl

[32] P. Zhang; Z. Zhang On the free boundary problem of three-dimensional incompressible Euler equations, Comm. Pure Appl. Math, Volume 61, pp. 877-940 | MR | Zbl

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