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Volumn 219, Issue 1, 2006, Pages 40-59

Nature of complex singularities for the 2D Euler equation

Author keywords

Euler equation; Singularities

Indexed keywords

ASYMPTOTIC STABILITY; FOURIER TRANSFORMS; FUNCTION EVALUATION; WAVE EQUATIONS;

EID: 33745753714     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.05.011     Document Type: Article
Times cited : (36)

References (39)
  • 1
    • 33745737381 scopus 로고    scopus 로고
    • And it bubbles and seethes, and it hisses and roars, As when fire is with water commix'd and contending, And the spray of its wrath to the welkin up-soars, And flood upon flood hurries on, never-ending (translation by Edward, Lord Lytton)
  • 4
    • 3543151404 scopus 로고    scopus 로고
    • Singularities of the Euler equation? Not out of the blue!
    • Frisch U., Matsumoto T., and Bec J. Singularities of the Euler equation? Not out of the blue!. J. Stat. Phys. 113 (2003) 761-781
    • (2003) J. Stat. Phys. , vol.113 , pp. 761-781
    • Frisch, U.1    Matsumoto, T.2    Bec, J.3
  • 5
    • 0000333210 scopus 로고
    • Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompresiblen Flüssigkeit
    • Hölder E. Über die unbeschränkte Fortsetzbarkeit einer stetigen ebenen Bewegung in einer unbegrenzten inkompresiblen Flüssigkeit. Math. Z. 37 (1933) 727-738
    • (1933) Math. Z. , vol.37 , pp. 727-738
    • Hölder, E.1
  • 6
    • 34250940791 scopus 로고
    • Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long
    • Wolibner W. Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long. Math. Z. 37 (1933) 698-726
    • (1933) Math. Z. , vol.37 , pp. 698-726
    • Wolibner, W.1
  • 7
    • 0010805768 scopus 로고
    • Analyticité des solutions périodiques de l'équation d'Euler en deux dimensions
    • Bardos C., Benachour S., and Zerner M. Analyticité des solutions périodiques de l'équation d'Euler en deux dimensions. C. R. Acad. Sci. Paris 282 A (1976) 995-998
    • (1976) C. R. Acad. Sci. Paris , vol.282 A , pp. 995-998
    • Bardos, C.1    Benachour, S.2    Zerner, M.3
  • 8
    • 0010814938 scopus 로고
    • Analyticité des solutions de l'équation d'Euler en trois dimensions
    • Benachour S. Analyticité des solutions de l'équation d'Euler en trois dimensions. C. R. Acad. Sci. Paris 283 A (1976) 107-110
    • (1976) C. R. Acad. Sci. Paris , vol.283 A , pp. 107-110
    • Benachour, S.1
  • 9
    • 3543088612 scopus 로고
    • Analyticité des solutions des équations d'Euler
    • Benachour S. Analyticité des solutions des équations d'Euler. Arch. Ration. Mech. Anal. 71 (1976) 271-299
    • (1976) Arch. Ration. Mech. Anal. , vol.71 , pp. 271-299
    • Benachour, S.1
  • 10
    • 0001140293 scopus 로고
    • Tracing complex singularities with spectral methods
    • Sulem C., Sulem P.L., and Frisch H. Tracing complex singularities with spectral methods. J. Comput. Phys. 50 (1983) 138-161
    • (1983) J. Comput. Phys. , vol.50 , pp. 138-161
    • Sulem, C.1    Sulem, P.L.2    Frisch, H.3
  • 12
    • 18844400628 scopus 로고    scopus 로고
    • The analytic structure of 2D Euler flow at short times
    • Matsumoto T., Bec J., and Frisch U. The analytic structure of 2D Euler flow at short times. Fluid Dyn. Res. 36 (2005) 221-237
    • (2005) Fluid Dyn. Res. , vol.36 , pp. 221-237
    • Matsumoto, T.1    Bec, J.2    Frisch, U.3
  • 13
    • 0001410755 scopus 로고
    • Mechanism of the production of small eddies from large ones
    • Taylor G.I., and Green A.E. Mechanism of the production of small eddies from large ones. Proc. R. Soc. A 158 (1937) 499-521
    • (1937) Proc. R. Soc. A , vol.158 , pp. 499-521
    • Taylor, G.I.1    Green, A.E.2
  • 15
    • 0022076997 scopus 로고
    • Three-dimensional periodic flows with high-symmetry
    • Kida S. Three-dimensional periodic flows with high-symmetry. J. Phys. Soc. Japan 54 (1985) 2132-2136
    • (1985) J. Phys. Soc. Japan , vol.54 , pp. 2132-2136
    • Kida, S.1
  • 16
    • 6144230088 scopus 로고    scopus 로고
    • Evidence for a real-time singularity in hydrodynamics from time series analysis
    • Pelz R.B., and Gulak Y. Evidence for a real-time singularity in hydrodynamics from time series analysis. Phys. Rev. Lett. 79 (1997) 4998-5001
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 4998-5001
    • Pelz, R.B.1    Gulak, Y.2
  • 17
    • 18844420865 scopus 로고    scopus 로고
    • Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows
    • Cichowlas C., and Brachet M.E. Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows. Fluid Dyn. Res. 36 (2005) 239-248
    • (2005) Fluid Dyn. Res. , vol.36 , pp. 239-248
    • Cichowlas, C.1    Brachet, M.E.2
  • 18
    • 0027473322 scopus 로고
    • Singularities of the Euler equation and hydrodynamic stability
    • Tanveer S., and Speziale C.G. Singularities of the Euler equation and hydrodynamic stability. Phys. Fluids A 5 (1993) 1456-1465
    • (1993) Phys. Fluids A , vol.5 , pp. 1456-1465
    • Tanveer, S.1    Speziale, C.G.2
  • 19
    • 43949163593 scopus 로고
    • Singularity formation for complex solutions of the 3D incompressible Euler equation
    • Caflisch R.E. Singularity formation for complex solutions of the 3D incompressible Euler equation. Physica D 67 (1993) 1-18
    • (1993) Physica D , vol.67 , pp. 1-18
    • Caflisch, R.E.1
  • 20
    • 0026809542 scopus 로고
    • A study of singularity formation in vortex sheet motion by a spectrally accurate vortex method
    • Shelley M.J. A study of singularity formation in vortex sheet motion by a spectrally accurate vortex method. J. Fluid Mech. 244 (1992) 493-526
    • (1992) J. Fluid Mech. , vol.244 , pp. 493-526
    • Shelley, M.J.1
  • 21
    • 0022735928 scopus 로고
    • A study of singularity formation in a vortex sheet by the point-vortex approximation
    • Krasny R. A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167 (1986) 65-93
    • (1986) J. Fluid Mech. , vol.167 , pp. 65-93
    • Krasny, R.1
  • 22
    • 0004082133 scopus 로고
    • The Painlevé property for partial differential equations
    • Weiss J., Tabor M., and Carnevale G. The Painlevé property for partial differential equations. J. Math. Phys. 24 (1983) 552-559
    • (1983) J. Math. Phys. , vol.24 , pp. 552-559
    • Weiss, J.1    Tabor, M.2    Carnevale, G.3
  • 23
    • 0013731938 scopus 로고
    • The spontaneous appearance of a singularity in the shape of an evolving vortex sheet
    • Moore D.W. The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. R. Soc. Lond. A 365 (1979) 105-119
    • (1979) Proc. R. Soc. Lond. A , vol.365 , pp. 105-119
    • Moore, D.W.1
  • 25
    • 84956104815 scopus 로고
    • Conditions for absolute convergence of series of Taylor coefficients of meromorphic functions of two variables
    • Tsikh A.K. Conditions for absolute convergence of series of Taylor coefficients of meromorphic functions of two variables. Math. USSR Sbornik 74 (1993) 336-360
    • (1993) Math. USSR Sbornik , vol.74 , pp. 336-360
    • Tsikh, A.K.1
  • 26
    • 33745739623 scopus 로고
    • On asymptotics of Taylor coefficients of rational functions of two variables
    • (translated from: Izv. Vuzov Mat. 37 (6) (1993) 26-33)
    • Orlov A.G. On asymptotics of Taylor coefficients of rational functions of two variables. Russian Math. (Iz. Vuz) 37 6 (1993) 23-30 (translated from: Izv. Vuzov Mat. 37 (6) (1993) 26-33)
    • (1993) Russian Math. (Iz. Vuz) , vol.37 , Issue.6 , pp. 23-30
    • Orlov, A.G.1
  • 27
    • 33745756416 scopus 로고
    • About asymptotics of Taylor coefficients of algebraic functions
    • (in Russian)
    • Orlov A.G. About asymptotics of Taylor coefficients of algebraic functions. Siberian Math. J. 35 (1994) 1125-1137 (in Russian)
    • (1994) Siberian Math. J. , vol.35 , pp. 1125-1137
    • Orlov, A.G.1
  • 28
    • 33745746249 scopus 로고    scopus 로고
    • D.H. Bailey, A fortran-90 based multiprecision system, RNR Technical Report, RNR-94-013, 1995. See also http://crd.lbl.gov/~dhbailey/
  • 29
    • 84968468830 scopus 로고
    • The rational approximation of functions which are formally defined by a power series expansion
    • Wynn P. The rational approximation of functions which are formally defined by a power series expansion. Math. Comput. 14 (1960) 147-186
    • (1960) Math. Comput. , vol.14 , pp. 147-186
    • Wynn, P.1
  • 30
    • 85171863190 scopus 로고
    • Non-linear transformations of divergent and slowly convergent
    • Shanks D. Non-linear transformations of divergent and slowly convergent. sequences, J. Math. Phys. 34 (1955) 1-42
    • (1955) sequences, J. Math. Phys. , vol.34 , pp. 1-42
    • Shanks, D.1
  • 31
    • 33745741931 scopus 로고    scopus 로고
    • J. van der Hoeven, Algorithms for asymptotic interpolation, J. Symbolic Comput. (2006) (submitted for publication). Preprint 2006-12 Dep. Math. Univ. Paris-Sud. See also http://www.math.u-psud.fr/~vdhoeven/Publs/2006/interpolate.ps.gz
  • 35
    • 14844359185 scopus 로고    scopus 로고
    • Lagrangian singularities of steady two-dimensional flows
    • Pauls W., and Matsumoto T. Lagrangian singularities of steady two-dimensional flows. Geophys. Astrophys. Fluid Dyn. 99 (2005) 61-75
    • (2005) Geophys. Astrophys. Fluid Dyn. , vol.99 , pp. 61-75
    • Pauls, W.1    Matsumoto, T.2
  • 37
  • 39
    • 0037331593 scopus 로고    scopus 로고
    • Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box
    • Kaneda Y., Ishihara T., Yokokawa M., Itakura K., and Uno A. Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15 (2003) L21-L42
    • (2003) Phys. Fluids , vol.15
    • Kaneda, Y.1    Ishihara, T.2    Yokokawa, M.3    Itakura, K.4    Uno, A.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.