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Volumn 199, Issue 2, 2011, Pages 653-705

Local Well-Posedness for Fluid Interface Problems

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EID: 78751704957     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-010-0335-5     Document Type: Article
Times cited : (149)

References (32)
  • 1
    • 1342266714 scopus 로고    scopus 로고
    • Well-posedness of vortex sheets with surface tension
    • Ambrose D. M.: Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 35(1), 211-244 (2003).
    • (2003) SIAM J. Math. Anal. , vol.35 , Issue.1 , pp. 211-244
    • Ambrose, D.M.1
  • 2
    • 26944460000 scopus 로고    scopus 로고
    • The zero surface tension limit of two-dimensional water waves
    • Ambrose D. M., Masmoudi N.: The zero surface tension limit of two-dimensional water waves. Commun. Pure Appl. Math. 58(10), 1287-1315 (2005).
    • (2005) Commun. Pure Appl. Math. , vol.58 , Issue.10 , pp. 1287-1315
    • Ambrose, D.M.1    Masmoudi, N.2
  • 3
    • 34547194744 scopus 로고    scopus 로고
    • Well-posedness of 3D vortex sheets with surface tension
    • Ambrose D. M., Masmoudi N.: Well-posedness of 3D vortex sheets with surface tension. Commun. Math. Sci. 5(2), 391-430 (2007).
    • (2007) Commun. Math. Sci. , vol.5 , Issue.2 , pp. 391-430
    • Ambrose, D.M.1    Masmoudi, N.2
  • 4
    • 0001356905 scopus 로고
    • Sur la gèométrie diffèrentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • Arnold V. I.: Sur la gèométrie diffèrentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16, 316-361 (1966).
    • (1966) Ann. Inst. Fourier , vol.16 , pp. 316-361
    • Arnold, V.I.1
  • 5
    • 84990576574 scopus 로고
    • Growth rates for the linearized motion of fluid interfaces away from equilibrium
    • Beale J. T., Hou T. Y., Lowengrub J. S.: Growth rates for the linearized motion of fluid interfaces away from equilibrium. Commun. Pure Appl. Math. 46(9), 1269-1301 (1993).
    • (1993) Commun. Pure Appl. Math. , vol.46 , Issue.9 , pp. 1269-1301
    • Beale, J.T.1    Hou, T.Y.2    Lowengrub, J.S.3
  • 6
    • 0032136390 scopus 로고    scopus 로고
    • On the Cauchy problem for a capillary drop. I. Irrotational motion
    • Beyer, K., Günther, M.: On the Cauchy problem for a capillary drop. I. Irrotational motion. Math. Methods Appl. Sci. 21(12), 1149-1183.
    • Math. Methods Appl. Sci. , vol.21 , Issue.12 , pp. 1149-1183
    • Beyer, K.1    Günther, M.2
  • 7
    • 17444410916 scopus 로고    scopus 로고
    • The Jacobi equation for irrotational free boundary flows
    • Beyer K., Günther M.: The Jacobi equation for irrotational free boundary flows. Analysis (Munich) 20(3), 237-254 (2007).
    • (2007) Analysis (Munich) , vol.20 , Issue.3 , pp. 237-254
    • Beyer, K.1    Günther, M.2
  • 8
    • 0033483717 scopus 로고    scopus 로고
    • Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations
    • Brenier Y.: Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Commun. Pure Appl. Math. 52(4), 411-452 (1999).
    • (1999) Commun. Pure Appl. Math. , vol.52 , Issue.4 , pp. 411-452
    • Brenier, Y.1
  • 9
    • 84990556256 scopus 로고
    • Long time existence for a slightly perturbed vortex sheet
    • Caflisch R. E., Orellana O. F.: Long time existence for a slightly perturbed vortex sheet. Commun. Pure Appl. Math. 39(6), 807-838 (1986).
    • (1986) Commun. Pure Appl. Math. , vol.39 , Issue.6 , pp. 807-838
    • Caflisch, R.E.1    Orellana, O.F.2
  • 10
    • 55749106935 scopus 로고    scopus 로고
    • On the motion of vortex sheets with surface tension in the 3D Euler equations with vorticity
    • Cheng C.-H., Coutand D., Shkoller S.: On the motion of vortex sheets with surface tension in the 3D Euler equations with vorticity. Commun. Pure Appl. Math. 61(12), 1715-1752 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.12 , pp. 1715-1752
    • Cheng, C.-H.1    Coutand, D.2    Shkoller, S.3
  • 11
    • 0034368951 scopus 로고    scopus 로고
    • On the motion of the free surface of a liquid
    • Christodoulou D., Lindblad H.: On the motion of the free surface of a liquid. Commun. Pure Appl. Math. 53(12), 1536-1602 (2000).
    • (2000) Commun. Pure Appl. Math. , vol.53 , Issue.12 , pp. 1536-1602
    • Christodoulou, D.1    Lindblad, H.2
  • 12
    • 34548446988 scopus 로고    scopus 로고
    • Well posedness of the free-surface incompressible Euler equations with or without surface tension
    • Coutand D., Shkoller S.: Well posedness of the free-surface incompressible Euler equations with or without surface tension. J. Am. Math. Soc. 20(3), 829-930 (2007).
    • (2007) J. Am. Math. Soc. , vol.20 , Issue.3 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 13
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
    • Craig W.: An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Comm. Partial Diff. Equ. 10(8), 787-1003 (1985).
    • (1985) Comm. Partial Diff. Equ. , vol.10 , Issue.8 , pp. 787-1003
    • Craig, W.1
  • 14
    • 0001547709 scopus 로고
    • Variation principles of hydrodynamics
    • Eckart C.: Variation principles of hydrodynamics. Phys. Fluids 3, 421-427 (1960).
    • (1960) Phys. Fluids , vol.3 , pp. 421-427
    • Eckart, C.1
  • 15
    • 0011555392 scopus 로고
    • The equations of motion of a perfect fluid with free boundary are not well posed
    • Ebin D.: The equations of motion of a perfect fluid with free boundary are not well posed. Commun. Part. Diff. Equ. 10, 1175-1201 (1987).
    • (1987) Commun. Part. Diff. Equ. , vol.10 , pp. 1175-1201
    • Ebin, D.1
  • 16
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the notion of an incompressible fluid
    • Ebin D. G., Marsden G.: Groups of diffeomorphisms and the notion of an incompressible fluid. Ann. Math. (2) 92, 102-163 (1970).
    • (1970) Ann. Math. (2) , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, G.2
  • 17
    • 84971113623 scopus 로고
    • The derivation of the equations of motion of an ideal fluid by Hamilton's principle
    • Herivel J. W.: The derivation of the equations of motion of an ideal fluid by Hamilton's principle. Proc. Cambridge Phil. Soc. 51, 344-349 (1955).
    • (1955) Proc. Cambridge Phil. Soc. , vol.51 , pp. 344-349
    • Herivel, J.W.1
  • 18
    • 0031522531 scopus 로고    scopus 로고
    • On the two-phase free boundary problem for two-dimensional water waves
    • Iguchi T., Tanaka N., Tani A.: On the two-phase free boundary problem for two-dimensional water waves. Math. Ann. 309(2), 199-223 (1997).
    • (1997) Math. Ann. , vol.309 , Issue.2 , pp. 199-223
    • Iguchi, T.1    Tanaka, N.2    Tani, A.3
  • 19
    • 22544482964 scopus 로고    scopus 로고
    • Well-posedness of the water-waves equations
    • Lannes D.: Well-posedness of the water-waves equations. J. Am. Math. Soc. 18, 605-654 (2005).
    • (2005) J. Am. Math. Soc. , vol.18 , pp. 605-654
    • Lannes, D.1
  • 20
    • 26044448758 scopus 로고    scopus 로고
    • Well-posedness for the motion of an incompressible liquid with free surface boundary
    • Lindblad H.: Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. Math. 162(1), 109-194 (2005).
    • (2005) Ann. Math. , vol.162 , Issue.1 , pp. 109-194
    • Lindblad, H.1
  • 21
    • 0000306561 scopus 로고
    • The Cauchy-Poisson problem. (Russian) Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod
    • Nalimov V. I.: The Cauchy-Poisson problem. (Russian) Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod. Granicami 10-210, 254 (1974).
    • (1974) Granicami , vol.10-210 , pp. 254
    • Nalimov, V.I.1
  • 23
    • 52349104032 scopus 로고    scopus 로고
    • Geometry and a priori estimates for free boundary problems of the Euler's equation
    • Shatah J., Zeng C.: Geometry and a priori estimates for free boundary problems of the Euler's equation. Commun. Pure Appl. Math. 51(5), 698-744 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.51 , Issue.5 , pp. 698-744
    • Shatah, J.1    Zeng, C.2
  • 24
    • 52349092767 scopus 로고    scopus 로고
    • A priori estimates for fluid interface problems
    • Shatah J., Zeng C.: A priori estimates for fluid interface problems. Commun. Pure Appl. Math. 61(6), 848-876 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.6 , pp. 848-876
    • Shatah, J.1    Zeng, C.2
  • 25
    • 0002479515 scopus 로고
    • The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid. (Russian)
    • Shnirelman, A.: The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid. (Russian) Mat. Sb. (N. S.) 128 (170), no. 1, 82-109, 144 (1985).
    • (1985) Mat. Sb. (N. S.) , vol.128-170 , Issue.1
    • Shnirelman, A.1
  • 26
    • 25644455336 scopus 로고    scopus 로고
    • On the three-dimensional Euler equations with a free boundary subject to surface tension
    • Schweizer B.: On the three-dimensional Euler equations with a free boundary subject to surface tension. Ann. Inst. H. Poincare. Anal. Non Lineaire 22(6), 753-781 (2005).
    • (2005) Ann. Inst. H. Poincare. Anal. Non Lineaire , vol.22 , Issue.6 , pp. 753-781
    • Schweizer, B.1
  • 27
    • 0038247451 scopus 로고
    • Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability
    • Sulem C., Sulem P.-L., Bardos C., Frisch U.: Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability. Commun. Math. Phys. 80(4), 485-516 (1981).
    • (1981) Commun. Math. Phys. , vol.80 , Issue.4 , pp. 485-516
    • Sulem, C.1    Sulem, P.-L.2    Bardos, C.3    Frisch, U.4
  • 28
    • 0031506263 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 2-D
    • Wu S.: Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130(1), 39-72 (1997).
    • (1997) Invent. Math. , vol.130 , Issue.1 , pp. 39-72
    • Wu, S.1
  • 29
    • 0033446356 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 3-D
    • Wu S.: Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 12(2), 445-495 (1999).
    • (1999) J. Am. Math. Soc. , vol.12 , Issue.2 , pp. 445-495
    • Wu, S.1
  • 30
    • 85009585833 scopus 로고
    • Gravity waves on the free surface of an incompressible perfect fluid of finite depth
    • Yosihara H.: Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. Res. Inst. Math. Sci. 18(1), 49-96 (1982).
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , Issue.1 , pp. 49-96
    • Yosihara, H.1
  • 31
    • 0000375767 scopus 로고
    • Capillary-gravity waves for an incompressible ideal fluid
    • Yosihara H.: Capillary-gravity waves for an incompressible ideal fluid. J. Math. Kyoto Univ. 23(4), 649-694 (1983).
    • (1983) J. Math. Kyoto Univ. , vol.23 , Issue.4 , pp. 649-694
    • Yosihara, H.1
  • 32
    • 52349109943 scopus 로고    scopus 로고
    • On the free boundary problem of 3-D incompressible Euler equations
    • Zhang P., Zhang Z.: On the free boundary problem of 3-D incompressible Euler equations. Commun. Pure Appl. Math. 61(7), 877-940 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.7 , pp. 877-940
    • Zhang, P.1    Zhang, Z.2


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