메뉴 건너뛰기




Volumn 58, Issue 2, 2009, Pages 479-521

The zero surface tension limit of three-dimensional water waves

Author keywords

Surface tension; Vortex sheet; Water wave; Well posedness

Indexed keywords


EID: 67249144683     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2009.58.3450     Document Type: Article
Times cited : (87)

References (24)
  • 2
    • 34547194744 scopus 로고    scopus 로고
    • -, Well-posedness of 3D vortex sheets with surface tension, Commun. Math. Sci. 5 (2007), 391-430. MR 2334849 (2008g:76010)
    • -, Well-posedness of 3D vortex sheets with surface tension, Commun. Math. Sci. 5 (2007), 391-430. MR 2334849 (2008g:76010)
  • 3
    • 1342266714 scopus 로고    scopus 로고
    • D. M. AMBROSE, Well-posedness of vortex sheets with surface tension, SLAM J. Math. Anal. 35 (2003), 211-244 (electronic), http://dx.doi.org/10.1137/S0036141002403869. MR 2001473 (2005g:76006)
    • D. M. AMBROSE, Well-posedness of vortex sheets with surface tension, SLAM J. Math. Anal. 35 (2003), 211-244 (electronic), http://dx.doi.org/10.1137/S0036141002403869. MR 2001473 (2005g:76006)
  • 4
    • 0040438763 scopus 로고    scopus 로고
    • J. T. BEALE, A convergent boundary integral method for three-dimensional water waves, Math. Comp. 70 (2001), 977-1029. MR 1709144 (2001j:65141)
    • J. T. BEALE, A convergent boundary integral method for three-dimensional water waves, Math. Comp. 70 (2001), 977-1029. MR 1709144 (2001j:65141)
  • 5
    • 1542680901 scopus 로고    scopus 로고
    • Convergence of a boundary integral method for water waves
    • 98b:76009
    • 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, http://dx.doi.org/10.1137/S0036142993245750. MR 1411850 (98b:76009)
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 1797-1843
    • BEALE, J.T.1    HOU, T.Y.2    LOWENGRUB, J.3
  • 6
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • 85j:35154
    • J. T. BEALE, T. KATO, and A. MAJDA, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66, http://dx.doi.org/10.1007/BF01212349. MR 763762 (85j:35154)
    • (1984) Comm. Math. Phys , vol.94 , pp. 61-66
    • BEALE, J.T.1    KATO, T.2    MAJDA, A.3
  • 7
    • 0020191249 scopus 로고
    • Generalized vortex methods for free-surface flow problems
    • 84a:76002
    • G. R. BAKER, D. I. MEIRON, and S. A. ORSZAG, Generalized vortex methods for free-surface flow problems, J. Fluid Mech. 123 (1982), 477-501, http://dx.doi.org/10.1017/S0022112082003164. MR 687014 (84a:76002)
    • (1982) J. Fluid Mech , vol.123 , pp. 477-501
    • BAKER, G.R.1    MEIRON, D.I.2    ORSZAG, S.A.3
  • 9
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
    • 87f:35210
    • 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, http://dx.doi.org/10.1080/ 03605308508820396. MR 795808 (87f:35210)
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 787-1003
    • CRAIG, W.1
  • 10
    • 34548446988 scopus 로고    scopus 로고
    • D. COUTAND and S. SHKOLLER, Well-posedness of the free-surface incompressible Euler equa-tions with or without surface tension, J. Amer. Math. Soc. 20 (2007), 829-930 (electronic), http://dx.doi.org/10.1090/S0894-0347-07-00556-5. MR 2291920 (2008c:35242)
    • D. COUTAND and S. SHKOLLER, Well-posedness of the free-surface incompressible Euler equa-tions with or without surface tension, J. Amer. Math. Soc. 20 (2007), 829-930 (electronic), http://dx.doi.org/10.1090/S0894-0347-07-00556-5. MR 2291920 (2008c:35242)
  • 11
    • 0008283862 scopus 로고
    • Removing the stiffness from interfacial flows with surface tension
    • 95e:76069
    • T. Y. HOU, J. S. LOWENGRUB, and M. J. SHELLEY, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys. 114 (1994), 312-338, http://dx.doi.org/10.1006/jcph.1994. 1170. MR 1294935 (95e:76069)
    • (1994) J. Comput. Phys , vol.114 , pp. 312-338
    • HOU, T.Y.1    LOWENGRUB, J.S.2    SHELLEY, M.J.3
  • 12
    • 0030870172 scopus 로고    scopus 로고
    • The long-time motion of vortex sheets with surface tension
    • 98d:76033
    • -, The long-time motion of vortex sheets with surface tension, Phys. Fluids 9 (1997), 1933-1954, http://dx.doi.org/10.1063/1.869313. MR 1455083 (98d:76033)
    • (1997) Phys. Fluids , vol.9 , pp. 1933-1954
    • HOU, T.Y.1    LOWENGRUB, J.S.2    SHELLEY, M.J.3
  • 13
    • 0013315837 scopus 로고    scopus 로고
    • T. Y. HOU and P. ZHANG, Convergence of a boundary integral method for 3-D water waves, Discrete Contin. Dyn. Syst. Ser. B 2 (2002), 1-34. MR 1877037 (2003k:76097)
    • T. Y. HOU and P. ZHANG, Convergence of a boundary integral method for 3-D water waves, Discrete Contin. Dyn. Syst. Ser. B 2 (2002), 1-34. MR 1877037 (2003k:76097)
  • 14
    • 0031522531 scopus 로고    scopus 로고
    • On the two-phase free boundary problem for two-dimensional water waves
    • 98e:76015
    • T. IGUCHI, N. TANAKA, and A. TANI, On the two-phase free boundary problem for two-dimensional water waves, Math. Ann. 309 (1997), 199-223, http://dx.doi.org/10.1007/s002080050110. MR 1474190 (98e:76015)
    • (1997) Math. Ann , vol.309 , pp. 199-223
    • IGUCHI, T.1    TANAKA, N.2    TANI, A.3
  • 15
    • 22544482964 scopus 로고    scopus 로고
    • D. LANNES, Well-posedness of the water-waves equations, J. Amer. Math. Soc. 18 (2005), 605-654 (electronic), http://dx.doi.org/ 10.1090/S0894-0347-05-00484-4. MR 2138139 (2005m:76021)
    • D. LANNES, Well-posedness of the water-waves equations, J. Amer. Math. Soc. 18 (2005), 605-654 (electronic), http://dx.doi.org/ 10.1090/S0894-0347-05-00484-4. MR 2138139 (2005m:76021)
  • 16
    • 26044448758 scopus 로고    scopus 로고
    • H. LINDBLAD, Well-posedness for the motion of an incompressible liquid with free surface boundary, Ann. of Math. (2) 162 (2005), 109-194. MR 2178961 (2006g:35293)
    • H. LINDBLAD, Well-posedness for the motion of an incompressible liquid with free surface boundary, Ann. of Math. (2) 162 (2005), 109-194. MR 2178961 (2006g:35293)
  • 19
    • 25644455336 scopus 로고    scopus 로고
    • B. SCHWEIZER, On the three-dimensional Euler equations with a free boundary sub-ject to surface tension, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), 753-781, http://dx.doi.org/10.1016/ j.anihpc.2004.11.001. MR 2172858 (2006g:35222)
    • B. SCHWEIZER, On the three-dimensional Euler equations with a free boundary sub-ject to surface tension, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), 753-781, http://dx.doi.org/10.1016/ j.anihpc.2004.11.001. MR 2172858 (2006g:35222)
  • 21
    • 0031506263 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 2-D
    • 98m:35167
    • S. WU, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math. 130 (1997), 39-72, http://dx.doi.org/10.1007/s002220050177. MR 1471885 (98m:35167)
    • (1997) Invent. Math , vol.130 , pp. 39-72
    • WU, S.1
  • 23
    • 85009585833 scopus 로고
    • Gravity waves on the free surface of an incompressible perfect fluid of finite depth
    • 83k:76017
    • H. YOSIHARA, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. Res. Inst. Math. Sci. 18 (1982), 49-96, http://dx.doi.org/10.2977/prims/1195184016. MR 660822 (83k:76017)
    • (1982) Publ. Res. Inst. Math. Sci , vol.18 , pp. 49-96
    • YOSIHARA, H.1
  • 24
    • 84875102840 scopus 로고    scopus 로고
    • -, Capillary-gravity waves for an incompressible ideal fluid, J. Math. Kyoto Univ. 23 (1983), 649-694. MR 728155 (85i:76011) [25] P. ZHANG and Z. ZHANG, On the free boundary problem of 3-D incompressible Euler equations (2006) (preprint).
    • -, Capillary-gravity waves for an incompressible ideal fluid, J. Math. Kyoto Univ. 23 (1983), 649-694. MR 728155 (85i:76011) [25] P. ZHANG and Z. ZHANG, On the free boundary problem of 3-D incompressible Euler equations (2006) (preprint).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.