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Volumn 178, Issue 3, 2013, Pages 1061-1134

Finite time singularities for the free boundary incompressible euler equations

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EID: 84884318144     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2013.178.3.6     Document Type: Article
Times cited : (124)

References (35)
  • 1
    • 79959880152 scopus 로고    scopus 로고
    • On the water-wave equations with surface tension
    • MR 2805065. Zbl 1258.35043
    • T. Alazard, N. Burq, and C. Zuily, On the water-wave equations with surface tension, Duke Math. J. 158 (2011), 413{499. MR 2805065. Zbl 1258.35043. http://dx.doi.org/10.1215/00127094-1345653.
    • (2011) Duke Math. J. , vol.158 , pp. 413-499
    • Alazard, T.1    Burq, N.2    Zuily, C.3
  • 2
    • 74949116792 scopus 로고    scopus 로고
    • Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves, Comm. Partial Differential Equations
    • MR 2581986. Zbl 1207.35082
    • T. Alazard and G. Métivier, Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves, Comm. Partial Differential Equations 34 (2009), 1632{1704. MR 2581986. Zbl 1207.35082. http://dx.doi.org/10.1080/03605300903296736.
    • (2009) , vol.34 , pp. 1632-1704
    • Alazard, T.1    Métivier, G.2
  • 3
    • 38349102793 scopus 로고    scopus 로고
    • Large time existence for 3D waterwaves and asymptotics
    • MR 2372806. Zbl 1131.76012
    • B. Alvarez-Samaniego and D. Lannes, Large time existence for 3D waterwaves and asymptotics, Invent. Math. 171 (2008), 485{541. MR 2372806. Zbl 1131.76012. http://dx.doi.org/10.1007/s00222-007-0088-4.
    • (2008) Invent. Math. , vol.171 , pp. 485-541
    • Alvarez-Samaniego, B.1    Lannes, D.2
  • 4
    • 26944460000 scopus 로고    scopus 로고
    • The zero surface tension limit of twodimensional water waves
    • MR 2162781. Zbl 1086.76004
    • D. M. Ambrose and N. Masmoudi, The zero surface tension limit of twodimensional water waves, Comm. Pure Appl. Math. 58 (2005), 1287{1315. MR 2162781. Zbl 1086.76004. http://dx.doi.org/10.1002/cpa.20085.
    • (2005) Comm. Pure Appl. Math. , vol.58 , pp. 1287-1315
    • Ambrose, D.M.1    Masmoudi, N.2
  • 5
    • 0020191249 scopus 로고
    • Generalized vortex methods for free-surface ow problems
    • MR 0687014. Zbl 0507.76028
    • G. R. Baker, D. I. Meiron, and S. A. Orszag, Generalized vortex methods for free-surface ow problems, J. Fluid Mech. 123 (1982), 477{501. MR 0687014. Zbl 0507.76028. http://dx.doi.org/10.1017/S0022112082003164.
    • (1982) J. Fluid Mech. , vol.123 , pp. 477-501
    • Baker, G.R.1    Meiron, D.I.2    Orszag, S.A.3
  • 6
    • 84990576574 scopus 로고
    • Growth rates for the linearized motion of uid interfaces away from equilibrium
    • MR 1231428. Zbl 0796.76041
    • J. T. Beale, T. Y. Hou, and J. S. Lowengrub, Growth rates for the linearized motion of uid interfaces away from equilibrium, Comm. Pure Appl. Math. 46 (1993), 1269{1301. MR 1231428. Zbl 0796.76041. http://dx.doi.org/10.1002/cpa.3160460903.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 1269-1301
    • Beale, J.T.1    Hou, T.Y.2    Lowengrub, J.S.3
  • 7
    • 1542680901 scopus 로고    scopus 로고
    • Convergence of a boundary integral method for water waves
    • MR 1411850. Zbl 0858.76046
    • 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. MR 1411850. Zbl 0858.76046. http://dx.doi.org/10.1137/S0036142993245750.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1797-1843
    • Beale, J.T.1    Hou, T.Y.2    Lowengrub, J.3
  • 9
    • 79953190074 scopus 로고    scopus 로고
    • Turning waves and breakdown for incompressible ows
    • MR 2792311. Zbl 1256.76019., USA,
    • A. Castro, D. Córdoba, C. L. Fefferman, F. Gancedo, and M. López- Fernáandez, Turning waves and breakdown for incompressible ows, Proc. Natl. Acad. Sci. USA 108 (2011), 4754{4759. MR 2792311. Zbl 1256.76019. http://dx.doi.org/10.1073/pnas.1101518108.
    • (2011) Proc. Natl. Acad. Sci. , vol.108 , pp. 4754-4759
    • Castro, A.1    Córdoba, D.2    Fefferman, C.L.3    Gancedo, F.4    López-Fernáandez, M.5
  • 10
    • 84857721683 scopus 로고    scopus 로고
    • Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
    • MR 2993754. Zbl 06025004
    • 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. 175 (2012), 909{948. MR 2993754. Zbl 06025004. http://dx.doi.org/10.4007/annals.2012.175.2.9.
    • (2012) Ann. of Math. , vol.175 , pp. 909-948
    • Castro, á.1    Córdoba, D.2    Fefferman, C.3    Gancedo, F.4    López-Fernández, M.5
  • 11
    • 84884340971 scopus 로고    scopus 로고
    • A naive parametrization for the vortex-sheet problem
    • in Mathematical Aspects of Fluid Mechanics, Cambridge Univ. Press, Cambridge
    • á. Castro, D. Córdoba, and F. Gancedo, A naive parametrization for the vortex-sheet problem, in Mathematical Aspects of Fluid Mechanics, Cambridge Univ. Press, Cambridge, 2012, pp. 88{115. http://dx.doi.org/10.1017/CBO9781139235792.006.
    • (2012) , vol.115 , pp. 88
    • Castro, á.1    Córdoba, D.2    Gancedo, F.3
  • 12
    • 0034368951 scopus 로고    scopus 로고
    • On the motion of the free surface of a liquid
    • MR 1780703. Zbl 1031. 35116
    • D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53 (2000), 1536{1602. MR 1780703. Zbl 1031. 35116. http://dx.doi.org/10.1002/1097-0312(200012)53:12h1536::AID-CPA2i3.0. CO;2-Q.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1536-1602
    • Christodoulou, D.1    Lindblad, H.2
  • 13
    • 70350325132 scopus 로고    scopus 로고
    • Interface evolution: water waves in 2-D
    • MR 2563213. Zbl 1183.35276
    • A. Córdoba, D. Córdoba, and F. Gancedo, Interface evolution: water waves in 2-D, Adv. Math. 223 (2010), 120{173. MR 2563213. Zbl 1183.35276. http://dx.doi.org/10.1016/j.aim.2009.07.016.
    • (2010) Adv. Math. , vol.223 , pp. 120-173
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 14
    • 78751624212 scopus 로고    scopus 로고
    • Interface evolution: the Hele- Shaw and Muskat problems
    • MR 2753607. Zbl 1229.35204
    • A. Córdoba, D. Córdoba, and F. Gancedo, Interface evolution: the Hele- Shaw and Muskat problems, Ann. of Math. 173 (2011), 477{542. MR 2753607. Zbl 1229.35204. http://dx.doi.org/10.4007/annals.2011.173.1.10.
    • (2011) Ann. of Math. , vol.173 , pp. 477-542
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 15
    • 84882688666 scopus 로고    scopus 로고
    • Porous media: the Muskat problem in three dimensions
    • MR 3071395
    • A. Córdoba, D. Córdoba, and F. Gancedo, Porous media: the Muskat problem in three dimensions, Anal. PDE 6 (2013), 447{497. MR 3071395. http://dx.doi.org/10.2140/apde.2013.6.447.
    • (2013) Anal. PDE , vol.6 , pp. 447-497
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 16
    • 34548446988 scopus 로고    scopus 로고
    • Well-posedness of the free-surface incompressible Euler equations with or without surface tension
    • MR 2291920. Zbl 1123.35038
    • D. Coutand and S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc. 20 (2007), 829{930. MR 2291920. Zbl 1123.35038. http://dx.doi.org/10.1090/S0894-0347-07-00556-5.
    • (2007) J. Amer. Math. Soc. , vol.20 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 17
    • 84870558141 scopus 로고    scopus 로고
    • On the finite-time splash singularity for the 3-D free-surface Euler equations
    • arXiv
    • D. Coutand and S. Shkoller, On the finite-time splash singularity for the 3-D free-surface Euler equations, 2012. arXiv 1201.4919.
    • (2012) , pp. 1201-4919
    • Coutand, D.1    Shkoller, S.2
  • 18
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
    • MR 0795808. Zbl 0577.76030
    • W. Craig, An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits, Comm. Partial Differential Equations 10 (1985), 787{1003. MR 0795808. Zbl 0577.76030. http://dx.doi.org/10.1080/03605308508820396.
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 787-1003
    • Craig, W.1
  • 19
    • 67650725448 scopus 로고    scopus 로고
    • Global solutions for the gravity water waves equation in dimension 3, C. R.
    • MR 2542891. Zbl 1177.35168
    • P. Germain, N. Masmoudi, and J. Shatah, Global solutions for the gravity water waves equation in dimension 3, C. R. Math. Acad. Sci. Paris 347 (2009), 897{902. MR 2542891. Zbl 1177.35168. http://dx.doi.org/10.1016/j.crma.2009.05.005.
    • (2009) Math. Acad. Sci. Paris , vol.347 , pp. 897-902
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 20
    • 84857870242 scopus 로고    scopus 로고
    • Global solutions for the gravity water waves equation in dimension 3
    • MR 2993751. Zbl 1241.35003
    • P. Germain, N. Masmoudi, and J. Shatah, Global solutions for the gravity water waves equation in dimension 3, Ann. of Math. 175 (2012), 691{754. MR 2993751. Zbl 1241.35003. http://dx.doi.org/10.4007/annals.2012.175.2.6.
    • (2012) Ann. of Math. , vol.175 , pp. 691-754
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 21
    • 22544482964 scopus 로고    scopus 로고
    • Well-posedness of the water-waves equations
    • MR 2138139. Zbl 1069.35056
    • D. Lannes, Well-posedness of the water-waves equations, J. Amer. Math. Soc. 18 (2005), 605{654. MR 2138139. Zbl 1069.35056. http://dx.doi.org/10.1090/S0894-0347-05-00484-4.
    • (2005) J. Amer. Math. Soc. , vol.18 , pp. 605-654
    • Lannes, D.1
  • 22
    • 84875533999 scopus 로고    scopus 로고
    • A stability criterion for two- uid interfaces and applications
    • MR 3035985. Zbl 06161067
    • D. Lannes, A stability criterion for two- uid interfaces and applications, Arch. Ration. Mech. Anal. 208 (2013), 481{567. MR 3035985. Zbl 06161067. http: //dx.doi.org/10.1007/s00205-012-0604-6.
    • (2013) Arch. Ration. Mech. Anal. , vol.208 , pp. 481-567
    • Lannes, D.1
  • 23
    • 26044448758 scopus 로고    scopus 로고
    • Well-posedness for the motion of an incompressible liquid with free surface boundary
    • MR 2178961. Zbl 1095. 35021
    • H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, Ann. of Math. 162 (2005), 109{194. MR 2178961. Zbl 1095. 35021. http://dx.doi.org/10.4007/annals.2005.162.109.
    • (2005) Ann. of Math. , vol.162 , pp. 109-194
    • Lindblad, H.1
  • 24
    • 0003236553 scopus 로고
    • Methods and Applications of Interval Analysis
    • 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, MR 0551212. Zbl 0417.65022
    • R. E. Moore, Methods and Applications of Interval Analysis, SIAM Stud. Appl. Math. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1979. MR 0551212. Zbl 0417.65022. http://dx.doi.org/10.1137/1.9781611970906.
    • (1979) SIAM Stud. Appl. Math.
    • Moore, R.E.1
  • 25
    • 0000306561 scopus 로고
    • The Cauchy-Poisson problem, Dinamika Splošn. Sredy
    • 254. MR 0609882
    • V. I. Nalimov, The Cauchy-Poisson problem, Dinamika Splošn. Sredy (1974), 104{210, 254. MR 0609882.
    • (1974) , pp. 104-210
    • Nalimov, V.I.1
  • 26
    • 84972536320 scopus 로고
    • An abstract form of the nonlinear Cauchy-Kowalewski theorem
    • collection of articles dedicated to S. S. Chern and D. C. Spencer on their sixtieth birthdays. MR 0322321. Zbl 0257. 35001
    • L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561{576, collection of articles dedicated to S. S. Chern and D. C. Spencer on their sixtieth birthdays. MR 0322321. Zbl 0257. 35001.
    • (1972) J. Differential Geometry , vol.6 , pp. 561-576
    • Nirenberg, L.1
  • 27
    • 84972513394 scopus 로고
    • A note on a theorem of Nirenberg
    • (1978). MR 0512931. Zbl 0368.35007. Available at
    • T. Nishida, A note on a theorem of Nirenberg, J. Differential Geom. 12 (1977), 629{633 (1978). MR 0512931. Zbl 0368.35007. Available at http://projecteuclid.org/euclid.jdg/1214434231.
    • (1977) J. Differential Geom. , vol.12 , pp. 629-633
    • Nishida, T.1
  • 28
    • 52349104032 scopus 로고    scopus 로고
    • Geometry and a priori estimates for free boundary problems of the Euler equation
    • MR 2388661. Zbl 1174.76001
    • J. Shatah and C. Zeng, Geometry and a priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math. 61 (2008), 698{744. MR 2388661. Zbl 1174.76001. http://dx.doi.org/10.1002/cpa.20213.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 698-744
    • Shatah, J.1    Zeng, C.2
  • 29
    • 84968512992 scopus 로고
    • Finite time analyticity for the two- and threedimensional Rayleigh-Taylor instability
    • MR 0766210. Zbl 0517.76051
    • C. Sulem and P.-L. Sulem, Finite time analyticity for the two- and threedimensional Rayleigh-Taylor instability, Trans. Amer. Math. Soc. 287 (1985), 127{160. MR 0766210. Zbl 0517.76051. http://dx.doi.org/10.2307/2000401.
    • (1985) Trans. Amer. Math. Soc. , vol.287 , pp. 127-160
    • Sulem, C.1    Sulem, P.-L.2
  • 30
    • 0031506263 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 2-D
    • MR 1471885. Zbl 0892.76009.
    • S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math. 130 (1997), 39{72. MR 1471885. Zbl 0892.76009. http://dx.doi.org/10.1007/s002220050177.
    • (1997) Invent. Math. , vol.130 , pp. 39-72
    • Wu, S.1
  • 31
    • 0033446356 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 3-D
    • MR 1641609. Zbl 0921.76017.
    • S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc. 12 (1999), 445{495. MR 1641609. Zbl 0921.76017. http://dx.doi.org/10.1090/S0894-0347-99-00290-8.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 445-495
    • Wu, S.1
  • 32
    • 67650433790 scopus 로고    scopus 로고
    • Almost global wellposedness of the 2-D full water wave problem
    • MR 2507638. Zbl 1181.35205
    • S. Wu, Almost global wellposedness of the 2-D full water wave problem, Invent. Math. 177 (2009), 45{135. MR 2507638. Zbl 1181.35205. http://dx.doi.org/10. 1007/s00222-009-0176-8.
    • (2009) Invent. Math. , vol.177 , pp. 45-135
    • Wu, S.1
  • 33
    • 79952989811 scopus 로고    scopus 로고
    • Global wellposedness of the 3-D full water wave problem
    • MR 2782254. Zbl 1221.35304
    • S. Wu, Global wellposedness of the 3-D full water wave problem, Invent. Math. 184 (2011), 125{220. MR 2782254. Zbl 1221.35304. http://dx.doi.org/10.1007/s00222-010-0288-1.
    • (2011) Invent. Math. , vol.184 , pp. 125-220
    • Wu, S.1
  • 34
    • 85009585833 scopus 로고
    • Gravity waves on the free surface of an incompressible perfect uid of finite depth
    • MR 0660822. Zbl 0493.76018.
    • H. Yosihara, Gravity waves on the free surface of an incompressible perfect uid of finite depth, Publ. Res. Inst. Math. Sci. 18 (1982), 49{96. MR 0660822. Zbl 0493.76018. http://dx.doi.org/10.2977/prims/1195184016.
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , pp. 49-96
    • Yosihara, H.1
  • 35
    • 52349109943 scopus 로고    scopus 로고
    • On the free boundary problem of three-dimensional incompressible Euler equations
    • MR 2410409. Zbl 1158.35107.
    • P. Zhang and Z. Zhang, On the free boundary problem of three-dimensional incompressible Euler equations, Comm. Pure Appl. Math. 61 (2008), 877{940. MR 2410409. Zbl 1158.35107. http://dx.doi.org/10.1002/cpa.20226.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 877-940
    • Zhang, P.1    Zhang, Z.2


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