메뉴 건너뛰기




Volumn 466, Issue 2121, 2010, Pages 2587-2604

Regularity and singularity in solutions of the three-dimensional Navier-Stokes equations

Author keywords

Intermittency; Navier Stokes; Regularity

Indexed keywords

THREE DIMENSIONAL; VISCOUS FLOW; VORTICITY;

EID: 77957198447     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0642     Document Type: Conference Paper
Times cited : (14)

References (38)
  • 1
    • 0001151111 scopus 로고
    • The nature of turbulent flow at large wave-numbers
    • doi:10.1098/rspa.1949.0136
    • Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent flow at large wave-numbers. Proc. R. Soc. Lond. A 199, 238-255. (doi:10.1098/rspa. 1949.0136)
    • (1949) Proc. R. Soc. Lond. A , vol.199 , pp. 238-255
    • Batchelor, G.K.1    Townsend, A.A.2
  • 2
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • doi:10.1007/BF01212349
    • Beale, J. T., Kato, T. & Majda, A. J. 1984 Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys. 94, 61-66. (doi:10.1007/BF01212349)
    • (1984) Commun. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.J.3
  • 3
    • 54749100842 scopus 로고    scopus 로고
    • Twenty-five years of multifractals in fully developed turbulence: A tribute to Giovanni Paladin
    • doi:10.1088/1751-8113/41/ 36/363001
    • Boffetta, G., Mazzino, A. & Vulpiani, A. 2008 Twenty-five years of multifractals in fully developed turbulence: a tribute to Giovanni Paladin. J. Phys. A 41, 363001. (doi:10.1088/1751-8113/41/ 36/363001)
    • (2008) J. Phys. A , vol.41 , pp. 363001
    • Boffetta, G.1    Mazzino, A.2    Vulpiani, A.3
  • 4
    • 84990576577 scopus 로고
    • Partial regularity of suitable weak solutions of the Navier-Stokes equations
    • doi:10.1002/cpa.3160350604
    • Caffarelli, L., Kohn, R. & Nirenberg, L. 1982 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math. 35, 771-831. (doi:10.1002/cpa.3160350604)
    • (1982) Commun. Pure Appl. Math. , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 5
    • 36348955539 scopus 로고    scopus 로고
    • Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
    • doi:10.4007/annals.2007.166.245
    • Cao, C. & Titi, E. S. 2007 Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Ann. Math. 166, 245-267. (doi:10.4007/annals.2007.166.245)
    • (2007) Ann. Math. , vol.166 , pp. 245-267
    • Cao, C.1    Titi, E.S.2
  • 6
    • 0001255802 scopus 로고    scopus 로고
    • On the singular set in the Navier-Stokes equations
    • doi:10.1006/jfan.2000.3582
    • Choe, H. J. & Lewis, J. L. 2000 On the singular set in the Navier-Stokes equations. J. Funct. Anal. 175, 348-369. (doi:10.1006/jfan.2000. 3582)
    • (2000) J. Funct. Anal. , vol.175 , pp. 348-369
    • Choe, H.J.1    Lewis, J.L.2
  • 7
    • 0000646280 scopus 로고
    • Direction of vorticity and the problem of global regularity for the Navier-Stokes equations
    • doi:10.1512/iumj.1993.42.42034
    • Constantin, P. & Fefferman, C. 1993 Direction of vorticity and the problem of global regularity for the Navier-Stokes equations. Indiana Univ. Math. J. 42, 775-789. (doi:10.1512/ iumj.1993.42.42034)
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 775-789
    • Constantin, P.1    Fefferman, C.2
  • 9
    • 0000385525 scopus 로고    scopus 로고
    • Geometric constraints on potentially singular solutions for the 3-D Euler equation
    • Constantin, P., Fefferman, Ch. & Majda, A. 1996 Geometric constraints on potentially singular solutions for the 3-D Euler equation. Commun. Partial Diff. Equ. 21, 559-571.
    • (1996) Commun. Partial Diff. Equ. , vol.21 , pp. 559-571
    • Constantin, P.1    Fefferman, C.2    Majda, A.3
  • 10
    • 0037174473 scopus 로고    scopus 로고
    • Energy dissipation in body-forced turbulence
    • doi:10.1017/S0022112002001386
    • Doering, C. R. & Foias, C. 2002 Energy dissipation in body-forced turbulence. J. Fluid Mech. 467, 289-306. (doi:10.1017/S0022112002001386)
    • (2002) J. Fluid Mech. , vol.467 , pp. 289-306
    • Doering, C.R.1    Foias, C.2
  • 11
    • 0001042852 scopus 로고
    • Direct observation of the intermittency of intense vortex filaments in turbulence
    • doi:10.1103/PhysRevLett.67.983
    • Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vortex filaments in turbulence. Phys. Rev. Lett. 67, 983-986. (doi:10.1103/PhysRevLett.67.983)
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 983-986
    • Douady, S.1    Couder, Y.2    Brachet, M.E.3
  • 12
    • 0042597993 scopus 로고    scopus 로고
    • L3,8-solutions to the Navier-Stokes equations and backward uniqueness
    • Escauriaza, L., Seregin, G. A. & Sverak, V. 2003 L3,8-solutions to the Navier-Stokes equations and backward uniqueness. Usp. Matematicheskih Nauk 58, 3-44.
    • (2003) Usp. Matematicheskih Nauk , vol.58 , pp. 3-44
    • Escauriaza, L.1    Seregin, G.A.2    Sverak, V.3
  • 15
    • 84963487888 scopus 로고
    • New a priori estimates for Navier-Stokes equations in dimension 3
    • doi:10.1080/03605308108820180
    • Foias, C., Guillopé, C. & Temam, R. 1981 New a priori estimates for Navier-Stokes equations in dimension 3. Commun. Partial Diff. Equ. 6, 329-359. (doi:10.1080/03605308108820180)
    • (1981) Commun. Partial Diff. Equ. , vol.6 , pp. 329-359
    • Foias, C.1    Guillopé, C.2    Temam, R.3
  • 18
    • 33748792071 scopus 로고    scopus 로고
    • CKN theory of singularities of weak solutions of the Navier-Stokes equations
    • Lecture Notes in Mathematics. Berlin, Germany: Springer
    • Gallavotti, G. 2006 CKN theory of singularities of weak solutions of the Navier-Stokes equations. In Mathematical foundation of turbulent viscous flows. Lecture Notes in Mathematics, no. 1871, pp. 45-74. Berlin, Germany: Springer.
    • (2006) Mathematical Foundation of Turbulent Viscous Flows , Issue.1871 , pp. 45-74
    • Gallavotti, G.1
  • 19
    • 0002887501 scopus 로고
    • Well-posedness of the Euler and Navier-Stokes equations in the Lebesgue spaces Lsp(R2)
    • Kato, T. & Ponce, G. 1986 Well-posedness of the Euler and Navier-Stokes equations in the Lebesgue spaces Lsp(R2). Rev. Mat. IberoAm. 2, 73-88.
    • (1986) Rev. Mat. IberoAm. , vol.2 , pp. 73-88
    • Kato, T.1    Ponce, G.2
  • 20
    • 45849147737 scopus 로고    scopus 로고
    • On partial regularity for the Navier-Stokes equations
    • Kukavica, I. 2008a On partial regularity for the Navier-Stokes equations. Discret. Contin. Dyn. Syst. 21, 717-728.
    • (2008) Discret. Contin. Dyn. Syst. , vol.21 , pp. 717-728
    • Kukavica, I.1
  • 21
    • 59549091578 scopus 로고    scopus 로고
    • Regularity for the Navier-Stokes equations with a solution in a Morrey space
    • doi:10.1512/iumj.2008.57.3628
    • Kukavica, I. 2008b Regularity for the Navier-Stokes equations with a solution in a Morrey space. Indiana Univ. Math. J. 57, 2843-2860. (doi:10.1512/iumj.2008.57.3628)
    • (2008) Indiana Univ. Math. J. , vol.57 , pp. 2843-2860
    • Kukavica, I.1
  • 22
    • 84959586360 scopus 로고
    • Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid
    • doi:10.1017/S0022112071002581
    • Kuo, A. Y.-S. & Corrsin, S. 1971 Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid. J. Fluid Mech. 50, 285-320. (doi:10.1017/S0022112071002581)
    • (1971) J. Fluid Mech. , vol.50 , pp. 285-320
    • Kuo, A.Y.-S.1    Corrsin, S.2
  • 24
    • 0013198034 scopus 로고    scopus 로고
    • On partial regularity suitable weak solutions of the three dimensional Navier-Stokes equations
    • Ladyzhenskaya, O. & Seregin, G. 1999 On partial regularity suitable weak solutions of the three dimensional Navier-Stokes equations. J. Math. Fluid Mech. 1, 356-387.
    • (1999) J. Math. Fluid Mech. , vol.1 , pp. 356-387
    • Ladyzhenskaya, O.1    Seregin, G.2
  • 25
    • 51249193194 scopus 로고
    • Essai sur le mouvement d'un liquide visquex emplissant l'espace
    • doi:10.1007/BF02547354
    • Leray, J. 1934 Essai sur le mouvement d'un liquide visquex emplissant l'espace. Acta Math. 63, 193-248. (doi:10.1007/BF02547354)
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 26
    • 0032344639 scopus 로고    scopus 로고
    • A New Proof of the Caffarelli-Kohn-Nirenberg Theorem
    • DOI 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO;2-A
    • Lin, F. 1998 A new proof of the Caffarelli, Kohn and Nirenberg theorem. Commun. Pure Appl. Math. 51, 241-257. (doi:10.1002/(SICI)1097-0312(199803)51: 3<241::AID-CPA2>3.0.CO;2-A) (Pubitemid 128031986)
    • (1998) Communications on Pure and Applied Mathematics , vol.51 , Issue.3 , pp. 241-258
    • Lin, F.1
  • 27
    • 0026123844 scopus 로고
    • The multifractal nature of turbulent energy dissipation
    • doi:10.1017/S0022112091001830
    • Meneveau, C. & Sreenivasan, K. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429-484. (doi:10.1017/ S0022112091001830)
    • (1991) J. Fluid Mech. , vol.224 , pp. 429-484
    • Meneveau, C.1    Sreenivasan, K.2
  • 28
    • 34249290781 scopus 로고    scopus 로고
    • Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations
    • doi:10.1088/0951-7715/20/5/007
    • Robinson, J. C. & Sadowski, W. 2007 Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Nonlinearity 20, 1185-1191. (doi:10.1088/0951-7715/20/5/007)
    • (2007) Nonlinearity , vol.20 , pp. 1185-1191
    • Robinson, J.C.1    Sadowski, W.2
  • 29
    • 77957189665 scopus 로고    scopus 로고
    • Partial regularity results for solutions of the Navier-Stokes system
    • eds J. C. Robinson & J. L. Rodrigo. London Mathematical Society Series. Cambridge, UK: Cambridge University Press
    • Robinson, J. C. & Rodrigo, J. L. 2009 Partial regularity results for solutions of the Navier-Stokes system. In Partial differential equations and fluid mechanics (eds J. C. Robinson & J. L. Rodrigo). London Mathematical Society Series, pp. 121-145. Cambridge, UK: Cambridge University Press.
    • (2009) Partial Differential Equations and Fluid Mechanics , pp. 121-145
    • Robinson, J.C.1    Rodrigo, J.L.2
  • 30
    • 84972517978 scopus 로고
    • Partial regularity of solutions to the Navier-Stokes equations
    • Scheffer, V. 1976 Partial regularity of solutions to the Navier-Stokes equations. Pacific J. Math. 66, 535-552.
    • (1976) Pacific J. Math. , vol.66 , pp. 535-552
    • Scheffer, V.1
  • 31
    • 0001881423 scopus 로고
    • The Navier-Stokes equations on a bounded domain
    • doi:10.1007/BF01942692
    • Scheffer, V. 1980 The Navier-Stokes equations on a bounded domain. Commun. Math. Phys. 73, 1-42. (doi:10.1007/BF01942692)
    • (1980) Commun. Math. Phys. , vol.73 , pp. 1-42
    • Scheffer, V.1
  • 32
    • 17444430349 scopus 로고    scopus 로고
    • 3,∞-solutions to the Navier-Stokes equations up to boundary
    • DOI 10.1007/s00208-004-0625-z
    • Seregin, G. A. 2005 On smoothness of L3,8-solutions to the Navier-Stokes equations up to boundary. Math. Ann. 332, 219-238. (doi:10.1007/s00208-004-0625- z) (Pubitemid 40550204)
    • (2005) Mathematische Annalen , vol.332 , Issue.1 , pp. 219-238
    • Seregin, G.1
  • 33
    • 41449087909 scopus 로고    scopus 로고
    • Estimates of suitable weak solutions to the Navier-Stokes equations in critical Morrey spaces. [Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 336 (2006)]
    • 277
    • Seregin, G. A. 2006 Estimates of suitable weak solutions to the Navier-Stokes equations in critical Morrey spaces. [Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 336 (2006)]. Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 37, 199-210, 277.
    • (2006) Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. , vol.37 , pp. 199-210
    • Seregin, G.A.1
  • 34
    • 0001807443 scopus 로고
    • The initial value problem for the Navier-Stokes equations
    • ed. R. E. Langer. Madison, WI: University of Wisconsin Press
    • Serrin, J. 1963 The initial value problem for the Navier-Stokes equations. In Nonlinear problems (ed. R. E. Langer). Madison, WI: University of Wisconsin Press.
    • (1963) Nonlinear Problems
    • Serrin, J.1
  • 35
    • 0000372952 scopus 로고
    • Navier-Stokes equations and non-linear functional analysis
    • Philadelphia, PA: SIAM Press
    • Temam, R. 1995 Navier-Stokes equations and non-linear functional analysis. In CBMS-NSF Regional Conf. Series in Applied Mathematics, vol. 66. Philadelphia, PA: SIAM Press.
    • (1995) CBMS-NSF Regional Conf. Series in Applied Mathematics , vol.66
    • Temam, R.1
  • 36
    • 0000359176 scopus 로고    scopus 로고
    • Gradient estimation on Navier-Stokes equations
    • Tian, G. & Xin, Z. 1999 Gradient estimation on Navier-Stokes equations. Commun. Anal. Geom. 7, 221-257.
    • (1999) Commun. Anal. Geom. , vol.7 , pp. 221-257
    • Tian, G.1    Xin, Z.2
  • 37
    • 38649142859 scopus 로고    scopus 로고
    • A new proof of partial regularity of solutions to Navier-Stokes equations
    • doi:10.1007/s00030-007-6001-4
    • Vasseur, A. F. 2007 A new proof of partial regularity of solutions to Navier-Stokes equations. Nonlinear Diff. Equ. Appl. 14, 753-785. (doi:10.1007/s00030-007-6001-4)
    • (2007) Nonlinear Diff. Equ. Appl. , vol.14 , pp. 753-785
    • Vasseur, A.F.1
  • 38
    • 0037426874 scopus 로고    scopus 로고
    • Measuring intense rotation and dissipation in turbulent flows
    • DOI 10.1038/nature01334
    • Zeff, B. W., Lanterman, D. D., McAllister, R., Roy, R., Kostelich, E. J. & Lathrop, D. P. 2003 Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146-149. (doi:10.1038/nature01334) (Pubitemid 36090976)
    • (2003) Nature , vol.421 , Issue.6919 , pp. 146-149
    • Zeff, B.W.1    Lanterman, D.D.2    McAllister, R.3    Roy, R.4    Kostelich, E.J.5    Lathrop, D.P.6


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.