메뉴 건너뛰기




Volumn 206, Issue 2, 2011, Pages 363-403

A geometric approach to generalized Stokes conjectures

Author keywords

concentration compactness; frequency formula; singularity; Stokes conjecture; Water wave

Indexed keywords


EID: 79958782018     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11511-011-0066-y     Document Type: Article
Times cited : (52)

References (41)
  • 2
    • 33845404914 scopus 로고
    • Existence and regularity for a minimum problem with free boundary
    • Alt, H. W. & Caffarelli, L. A., Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math., 325 (1981), 105-144.
    • (1981) J. Reine Angew. Math. , vol.325 , pp. 105-144
    • Alt, H.W.1    Caffarelli, L.A.2
  • 3
    • 0000166670 scopus 로고
    • On the Stokes conjecture for the wave of extreme form
    • Amick, C. J., Fraenkel, L. E. & Toland, J. F., On the Stokes conjecture for the wave of extreme form. Acta Math., 148 (1982), 193-214.
    • (1982) Acta Math. , vol.148 , pp. 193-214
    • Amick, C.J.1    Fraenkel, L.E.2    Toland, J.F.3
  • 4
    • 0019656759 scopus 로고
    • On solitary water-waves of finite amplitude
    • Amick, C. J. & Toland, J. F., On solitary water-waves of finite amplitude. Arch. Ration. Mech. Anal., 76 (1981), 9-95.
    • (1981) Arch. Ration. Mech. Anal. , vol.76 , pp. 9-95
    • Amick, C.J.1    Toland, J.F.2
  • 5
    • 58449101312 scopus 로고    scopus 로고
    • A parabolic free boundary problem with Bernoulli type condition on the free boundary
    • Andersson, J. & Weiss, G. S., A parabolic free boundary problem with Bernoulli type condition on the free boundary. J. Reine Angew. Math., 627 (2009), 213-235.
    • (2009) J. Reine Angew. Math. , vol.627 , pp. 213-235
    • Andersson, J.1    Weiss, G.S.2
  • 6
    • 84966198519 scopus 로고
    • A free-boundary problem for the heat equation arising in flame propagation
    • Caffarelli, L. A. & Vázquez, J. L., A free-boundary problem for the heat equation arising in flame propagation. Trans. Amer. Math. Soc., 347 (1995), 411-441.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 411-441
    • Caffarelli, L.A.1    Vázquez, J.L.2
  • 7
    • 0018983231 scopus 로고
    • Numerical evidence for the existence of new types of gravity waves of permanent form on deep water
    • Chen, B. & Saffman, P. G., Numerical evidence for the existence of new types of gravity waves of permanent form on deep water. Stud. Appl. Math., 62 (1980), 1-21.
    • (1980) Stud. Appl. Math. , vol.62 , pp. 1-21
    • Chen, B.1    Saffman, P.G.2
  • 8
    • 1242319077 scopus 로고    scopus 로고
    • Exact steady periodic water waves with vorticity
    • Constantin, A. & Strauss, W., Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math., 57 (2004), 481-527.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 481-527
    • Constantin, A.1    Strauss, W.2
  • 10
    • 78650997048 scopus 로고    scopus 로고
    • Steady periodic water waves with constant vorticity: regularity and local bifurcation
    • Constantin, A. & Varvaruca, E., Steady periodic water waves with constant vorticity: regularity and local bifurcation. Arch. Ration. Mech. Anal., 199 (2011), 33-67.
    • (2011) Arch. Ration. Mech. Anal. , vol.199 , pp. 33-67
    • Constantin, A.1    Varvaruca, E.2
  • 11
    • 0003285448 scopus 로고
    • Weak Convergence Methods for Nonlinear Partial Differential Equations
    • Amer. Math. Soc., Providence, RI
    • Evans, L. C., Weak Convergence Methods for Nonlinear Partial Differential Equations. CBMS Regional Conference Series in Mathematics, 74. Amer. Math. Soc., Providence, RI, 1990.
    • (1990) CBMS Regional Conference Series in Mathematics , vol.74
    • Evans, L.C.1
  • 12
    • 84968518816 scopus 로고
    • Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity
    • Evans, L. C. & Müller, S., Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity. J. Amer. Math. Soc., 7 (1994), 199-219.
    • (1994) J. Amer. Math. Soc. , vol.7 , pp. 199-219
    • Evans, L.C.1    Müller, S.2
  • 13
    • 84990553387 scopus 로고
    • A remark about pointed bubbles
    • Garabedian, P. R., A remark about pointed bubbles. Comm. Pure Appl. Math., 38 (1985), 609-612.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 609-612
    • Garabedian, P.R.1
  • 14
    • 67650683389 scopus 로고    scopus 로고
    • Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem
    • Garofalo, N. & Petrosyan, A., Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem. Invent. Math., 177 (2009), 415-461.
    • (2009) Invent. Math. , vol.177 , pp. 415-461
    • Garofalo, N.1    Petrosyan, A.2
  • 15
    • 0003343498 scopus 로고
    • Minimal Surfaces and Functions of Bounded Variation
    • Birkhäuser, Basel
    • GiustiE., Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, 80 Birkhäuser, Basel, 1984.
    • (1984) Monographs in Mathematics , vol.80
    • Giusti, E.1
  • 16
    • 84971195530 scopus 로고
    • On the existence theory for irrotational water waves
    • Keady, G. & Norbury, J., On the existence theory for irrotational water waves. Math. Proc. Cambridge Philos. Soc., 83 (1978), 137-157.
    • (1978) Math. Proc. Cambridge Philos. Soc. , vol.83 , pp. 137-157
    • Keady, G.1    Norbury, J.2
  • 17
    • 0007191469 scopus 로고
    • On the theory of steady-state waves of finite amplitude
    • English translation in U. S. S. R. Comput. Math. and Math. Phys., 1 (1961), 996-1018
    • Krasovskiǐ, Yu. P., On the theory of steady-state waves of finite amplitude. Zh. Vychisl. Mat. i Mat. Fiz., 1 (1961), 836-855 (Russian). English translation in U. S. S. R. Comput. Math. and Math. Phys., 1 (1961), 996-1018.
    • (1961) Zh. Vychisl. Mat. i Mat. Fiz. , vol.1 , pp. 836-855
    • Krasovskiǐ, Y.P.1
  • 18
    • 0040250355 scopus 로고    scopus 로고
    • The Stokes and Krasovskii conjectures for the wave of greatest height
    • McLeod, J. B., The Stokes and Krasovskii conjectures for the wave of greatest height. Stud. Appl. Math., 98 (1997), 311-333.
    • (1997) Stud. Appl. Math. , vol.98 , pp. 311-333
    • McLeod, J.B.1
  • 19
    • 51249164666 scopus 로고
    • Partial regularity for weak solutions of a nonlinear elliptic equation
    • Pacard, F., Partial regularity for weak solutions of a nonlinear elliptic equation. Manuscripta Math., 79 (1993), 161-172.
    • (1993) Manuscripta Math. , vol.79 , pp. 161-172
    • Pacard, F.1
  • 20
    • 0013463858 scopus 로고
    • Justification of the Stokes conjecture in the theory of surface waves
    • English traslation in Stud. Appl. Math., 108 (2002), 217-244
    • Plotnikov, P. I., Justification of the Stokes conjecture in the theory of surface waves. Dinamika Sploshn. Sredy, 57 (1982), 41-76 (Russian). English traslation in Stud. Appl. Math., 108 (2002), 217-244.
    • (1982) Dinamika Sploshn. Sredy (Russian) , vol.57 , pp. 41-76
    • Plotnikov, P.I.1
  • 21
  • 22
    • 0010118943 scopus 로고
    • A monotonicity formula for Yang-Mills fields
    • Price, P., A monotonicity formula for Yang-Mills fields. Manuscripta Math., 43 (1983), 131-166.
    • (1983) Manuscripta Math. , vol.43 , pp. 131-166
    • Price, P.1
  • 24
    • 0002530417 scopus 로고
    • Analytic aspects of the harmonic map problem, in Seminar on Nonlinear Partial Differential Equations (Berkeley, CA, 1983)
    • Springer, New York
    • Schoen, R. M., Analytic aspects of the harmonic map problem, in Seminar on Nonlinear Partial Differential Equations (Berkeley, CA, 1983), Math. Sci. Res. Inst. Publ., 2, pp. 321-358. Springer, New York, 1984.
    • (1984) Math. Sci. Res. Inst. Publ. , vol.2 , pp. 321-358
    • Schoen, R.M.1
  • 26
    • 0014922691 scopus 로고
    • A variational principle for waves of infinite depth
    • Spielvogel, E. R., A variational principle for waves of infinite depth. Arch. Ration. Mech. Anal., 39 (1970), 189-205.
    • (1970) Arch. Ration. Mech. Anal. , vol.39 , pp. 189-205
    • Spielvogel, E.R.1
  • 27
    • 0000339396 scopus 로고
    • Considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form
    • Cambridge University Press, Cambridge
    • Stokes, G. G., Considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form, in Mathematical and Physical Papers, Vol. I, pp. 225-228. Cambridge University Press, Cambridge, 1880.
    • (1880) Mathematical and Physical Papers , vol.I , pp. 225-228
    • Stokes, G.G.1
  • 28
    • 0018030940 scopus 로고
    • On the existence of a wave of greatest height and Stokes's conjecture
    • Toland, J. F., On the existence of a wave of greatest height and Stokes's conjecture. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 363 (1978), 469-485.
    • (1978) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , vol.363 , pp. 469-485
    • Toland, J.F.1
  • 29
    • 0020507509 scopus 로고
    • Some new gravity waves in water of finite depth
    • Vanden-Broeck, J.-M., Some new gravity waves in water of finite depth. Phys. Fluids, 26 (1983), 2385-2387.
    • (1983) Phys. Fluids , vol.26 , pp. 2385-2387
    • Vanden-Broeck, J.-M.1
  • 30
    • 33748882598 scopus 로고    scopus 로고
    • Singularities of Bernoulli free boundaries
    • Varvaruca, E., Singularities of Bernoulli free boundaries. Comm. Partial Differential Equations, 31 (2006), 1451-1477.
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 1451-1477
    • Varvaruca, E.1
  • 31
    • 56049121441 scopus 로고    scopus 로고
    • Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth
    • Varvaruca, E. Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth. Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 1345-1362.
    • (2008) Proc. Roy. Soc. Edinburgh Sect. A , vol.138 , pp. 1345-1362
    • Varvaruca, E.1
  • 32
    • 63449141066 scopus 로고    scopus 로고
    • On the existence of extreme waves and the Stokes conjecture with vorticity
    • Varvaruca, E. On the existence of extreme waves and the Stokes conjecture with vorticity. J. Differential Equations, 246 (2009), 4043-4076.
    • (2009) J. Differential Equations , vol.246 , pp. 4043-4076
    • Varvaruca, E.1
  • 34
    • 59649099110 scopus 로고    scopus 로고
    • Steady water waves with a critical layer
    • Wahlén, E., Steady water waves with a critical layer. J. Differential Equations, 246 (2009), 2468-2483.
    • (2009) J. Differential Equations , vol.246 , pp. 2468-2483
    • Wahlén, E.1
  • 35
    • 0000747784 scopus 로고    scopus 로고
    • Partial regularity for weak solutions of an elliptic free boundary problem
    • Weiss, G. S., Partial regularity for weak solutions of an elliptic free boundary problem. Comm. Partial Differential Equations, 23 (1998), 439-455.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 439-455
    • Weiss, G.S.1
  • 36
    • 3042521971 scopus 로고    scopus 로고
    • Partial regularity for a minimum problem with free boundary
    • Weiss, G. S. Partial regularity for a minimum problem with free boundary. J. Geom. Anal., 9 (1999), 317-326.
    • (1999) J. Geom. Anal. , vol.9 , pp. 317-326
    • Weiss, G.S.1
  • 37
    • 0038675140 scopus 로고    scopus 로고
    • A singular limit arising in combustion theory: fine properties of the free boundary
    • Weiss, G. S. A singular limit arising in combustion theory: fine properties of the free boundary. Calc. Var. Partial Differential Equations, 17 (2003), 311-340.
    • (2003) Calc. Var. Partial Differential Equations , vol.17 , pp. 311-340
    • Weiss, G.S.1
  • 40
    • 67650433790 scopus 로고    scopus 로고
    • Almost global wellposedness of the 2-D full water wave problem
    • Wu, S. Almost global wellposedness of the 2-D full water wave problem. Invent. Math., 177 (2009), 45-135.
    • (2009) Invent. Math. , vol.177 , pp. 45-135
    • Wu, S.1
  • 41
    • 0023143878 scopus 로고
    • Nonsymmetric gravity waves on water of infinite depth
    • Zufiria, J. A., Nonsymmetric gravity waves on water of infinite depth. J. Fluid Mech., 181 (1987), 17-39.
    • (1987) J. Fluid Mech. , vol.181 , pp. 17-39
    • Zufiria, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.