Structural stability for the splash singularities of the water waves problem

Discrete and Continuous Dynamical Systems- Series A

Volumn 34, Issue 12, 2014, Pages 4997-5043

  Castro, Angel ^a   Córdoba, Diego ^b   Fefferman, Charles ^c   Gancedo, Francisco ^d   Gómez Serrano, Javier ^c  

^a INSTITUTO DE CIENCIAS MATEMÁTICAS   (Spain)

^b CSIC   (Spain)

^c PRINCETON UNIVERSITY   (United States)

^d UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Computer assisted; Contour dynamics; Euler equation; Splash singularity; Water waves

Indexed keywords

EID: 84902687851     PISSN: 10780947     EISSN: 15535231     Source Type: Journal    
DOI: 10.3934/dcds.2014.34.4997     Document Type: Article

References (9)

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.
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.
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.
4. A. 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.
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.
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, Ecole normale suṕerieure de Lyon, 2011.
9. D. Lannes, The Water Waves Problem: Mathematical Analysis and Asymptotics, Mathematical Surveys and Monographs. Amer Mathematical Society, 2013.