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Structural stability for the splash singularities of the water waves problem
1. | Departamento de Matemáticas de la UAM, Instituto de Ciencias Matemáticas del CSIC, Campus de Cantoblanco, 28049 Madrid |
2. | Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera, 13-15, 28049 Madrid |
3. | Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Road, Princeton, New Jersey 08544 |
4. | Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, Campus Reina Mercedes, 41012 Sevilla, Spain |
5. | Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Rd, Princeton, NJ 08544 |
References:
[1] |
J. T. Beale, T. Y. Hou and J. Lowengrub, Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal., 33 (1996), 1797-1843.
doi: 10.1137/S0036142993245750. |
[2] |
A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Splash singularity for water waves, Proceedings of the National Academy of Sciences, 109 (2012), 733-738.
doi: 10.1073/pnas.1115948108. |
[3] |
A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Finite time singularities for the free boundary incompressible Euler equations, Ann. of Math. (2), 178 (2013), 1061-1134.
doi: 10.4007/annals.2013.178.3.6. |
[4] |
Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo and M. López-Fernández, Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Ann. of Math. (2), 175 (2012), 909-948.
doi: 10.4007/annals.2012.175.2.9. |
[5] |
D. Coutand and S. Shkoller, On the finite-time splash and splat singularities for the 3-D free-surface Euler equations, Comm. Math. Phys., 325 (2014), 143-183.
doi: 10.1007/s00220-013-1855-2. |
[6] |
C. Fefferman, A. D. Ionescu and V. Lie, On the absence of "splash'' singularities in the case of two-fluid interfaces, arXiv preprint arXiv:1312.2917, 2013. |
[7] |
G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, second edition, 1995. |
[8] |
M. Joldes, Rigorous Polynomial Approximations and Applications, PhD thesis, École normale supérieure de Lyon, 2011. |
[9] |
D. Lannes, The Water Waves Problem: Mathematical Analysis and Asymptotics, Mathematical Surveys and Monographs. Amer Mathematical Society, 2013. |
show all references
References:
[1] |
J. T. Beale, T. Y. Hou and J. Lowengrub, Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal., 33 (1996), 1797-1843.
doi: 10.1137/S0036142993245750. |
[2] |
A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Splash singularity for water waves, Proceedings of the National Academy of Sciences, 109 (2012), 733-738.
doi: 10.1073/pnas.1115948108. |
[3] |
A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Finite time singularities for the free boundary incompressible Euler equations, Ann. of Math. (2), 178 (2013), 1061-1134.
doi: 10.4007/annals.2013.178.3.6. |
[4] |
Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo and M. López-Fernández, Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Ann. of Math. (2), 175 (2012), 909-948.
doi: 10.4007/annals.2012.175.2.9. |
[5] |
D. Coutand and S. Shkoller, On the finite-time splash and splat singularities for the 3-D free-surface Euler equations, Comm. Math. Phys., 325 (2014), 143-183.
doi: 10.1007/s00220-013-1855-2. |
[6] |
C. Fefferman, A. D. Ionescu and V. Lie, On the absence of "splash'' singularities in the case of two-fluid interfaces, arXiv preprint arXiv:1312.2917, 2013. |
[7] |
G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, second edition, 1995. |
[8] |
M. Joldes, Rigorous Polynomial Approximations and Applications, PhD thesis, École normale supérieure de Lyon, 2011. |
[9] |
D. Lannes, The Water Waves Problem: Mathematical Analysis and Asymptotics, Mathematical Surveys and Monographs. Amer Mathematical Society, 2013. |
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