@article{JEDP_2012____A2_0, author = {Fefferman, Charles}, title = {Formation of {Singularities} in {Fluid} {Interfaces}}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {2}, pages = {1--9}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2012}, doi = {10.5802/jedp.85}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.85/} }
TY - JOUR AU - Fefferman, Charles TI - Formation of Singularities in Fluid Interfaces JO - Journées équations aux dérivées partielles PY - 2012 SP - 1 EP - 9 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.85/ DO - 10.5802/jedp.85 LA - en ID - JEDP_2012____A2_0 ER -
Fefferman, Charles. Formation of Singularities in Fluid Interfaces. Journées équations aux dérivées partielles (2012), article no. 2, 9 p. doi : 10.5802/jedp.85. http://www.numdam.org/articles/10.5802/jedp.85/
[1] On the water-wave equations with surface tension, Duke Math. J., Volume 158 no. 3, pp. 413-499 | MR | Zbl
[2] The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math., Volume 58 no. 10, pp. 1287-1315 | MR | Zbl
[3] Large time existence for 3D water waves and asympotics, Invent. Math., Volume 171 no. 3, pp. 485-541 | MR | Zbl
[4] Global regularity for vortex patches, Comm. Pure Appl. Math., Volume 152 no. 1, pp. 19-28 | MR | Zbl
[5] Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal., Volume 33 no. 5, pp. 1797-1843 | MR | Zbl
[6] Finite time singularities for the free boundary incompressible Euler equations (preprint)
[7] Finite time singularities for water waves with surface tension (preprint)
[8] Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Annals of Math., Volume 175, pp. 909-948 | MR | Zbl
[9] Breakdown of smoothness for the Muskat problem (preprint)
[10] Interface evolution: Water waves in 2D, Adv. Math., Volume 223 no. 1, pp. 120-173 | Zbl
[11] On the global existence for the Muskat problem, JEMS, Volume 15 no. 1, pp. 201-227 | DOI | EuDML | MR | Zbl
[12] Evidence of singularities for a family of contour dynamics equations, Proc. Nat. Acad. Sci. USA, Volume 102, pp. 5949-5952 | MR | Zbl
[13] 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] Persistance de structures géometriques dans les fluides incompressibles bidimensionels, Ann. École Norm. Sup., Volume 26, pp. 1-16 | Numdam | MR | Zbl
[15] Global existence, singular solutions and ill-posedness for the Muskat problem, Comm. Pure Appl. Math, Volume 57, pp. 1374-1411 | MR | Zbl
[16] On the motion of the free surface of a liquid, Comm. Pure Appl. Math., Volume 53 no. 12, pp. 1536-1602 | MR | Zbl
[17] Global solutions for small data to the Hele-Shaw problem, Nonlinearity, Volume 6, pp. 393-415 | MR | Zbl
[18] On the finite-time splash singularity for the 3D free surface Euler equqations (preprint)
[19] 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] On the parabolicity of the Muskat problem: Well-posedness, fingering and stability results, Z. Annal. Awend, Volume 30, pp. 193-218 | MR | Zbl
[21] Existence for the -patch model and the sharp front in Sobolev spaces, Adv. Math., Volume 217, pp. 2569-2598 | MR | Zbl
[22] Global solutions for the gravity water waves equation in dimension 3, Annals of Math. | Zbl
[23] Well-posedness of the water-waves equation, J. Amer. Math. Soc., Volume 18 no. 3, pp. 605-654 | MR | Zbl
[24] Well-posedness for the motion of an incompressible liquid with free surface boundary, Annals of Math., Volume 162, pp. 109-194 | MR | Zbl
[25] On the evolution of sharp fronts for the quasigeostrophic equation, Comm. Pure Appl. Math., Volume 58 no. 6, pp. 821-866 | MR | Zbl
[26] 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] Almost global well-posedness of the 2D full water wave problem, Invent. Math., Volume 177 no. 1, pp. 45-135 | Zbl
[28] Global well-posedness of the 3D full water-wave problem, Invent. Math., Volume 184 no. 1, pp. 125-220 | Zbl
[29] Well-posedness in Sobolev spaces of the full water-wave problem in 2D, Invent. Math., Volume 177, pp. 39-72 | MR | Zbl
[30] 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] Global classical solution of Muskat free boundary problem, J. Math. Anal. Appl., Volume 288, pp. 442-461 | MR | Zbl
[32] 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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