메뉴 건너뛰기




Volumn 237, Issue 14-17, 2008, Pages 1926-1931

Singular, weak and absent: Solutions of the Euler equations

Author keywords

Blowup; Weak solutions

Indexed keywords

PHYSICS;

EID: 47049093520     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.01.006     Document Type: Article
Times cited : (26)

References (21)
  • 1
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • Beale J.T., Kato T., and Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys. 94 (1984) 61-66
    • (1984) Commun. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 2
    • 0028388187 scopus 로고
    • Geometric statistics in turbulence
    • Constantin P. Geometric statistics in turbulence. SIAM Rev. 36 (1994) 73-98
    • (1994) SIAM Rev. , vol.36 , pp. 73-98
    • Constantin, P.1
  • 3
    • 0000385525 scopus 로고    scopus 로고
    • Geometric constraints on potentially singular solutions for the 3-D Euler equations
    • Constantin P., Fefferman C., and Majda A. Geometric constraints on potentially singular solutions for the 3-D Euler equations. Commu. Partial Differential Equations 21 (1996) 559-571
    • (1996) Commu. Partial Differential Equations , vol.21 , pp. 559-571
    • Constantin, P.1    Fefferman, C.2    Majda, A.3
  • 5
    • 34248150423 scopus 로고    scopus 로고
    • Nonexistence of self-similar singularities for the 3D incompressible Euler equations
    • Chae D. Nonexistence of self-similar singularities for the 3D incompressible Euler equations. Commun. Math. Phys. 273 (2007) 203-215
    • (2007) Commun. Math. Phys. , vol.273 , pp. 203-215
    • Chae, D.1
  • 7
    • 17444395218 scopus 로고    scopus 로고
    • Geometric properties and non-blowup for 3-D incompressible Euler flow
    • Deng J., Hou T.Y., and Yu X. Geometric properties and non-blowup for 3-D incompressible Euler flow. Commu. Partial Differential Equations 30 (2005) 225-243
    • (2005) Commu. Partial Differential Equations , vol.30 , pp. 225-243
    • Deng, J.1    Hou, T.Y.2    Yu, X.3
  • 8
    • 0001212876 scopus 로고
    • Note on loss of regularity for solutions of the 3D incompressible Euler and related equations
    • Constantin P. Note on loss of regularity for solutions of the 3D incompressible Euler and related equations. Commun. Math. Phys. 106 (1986) 311-326
    • (1986) Commun. Math. Phys. , vol.106 , pp. 311-326
    • Constantin, P.1
  • 9
    • 51249193194 scopus 로고
    • Essai sur le mouvement d'un liquide visqueux emplissant l'espace
    • Leray J. Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934) 193-248
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 10
    • 47049093815 scopus 로고    scopus 로고
    • S. Resnick, Dynamical problems in nonlinear advective partial differential equations. Ph.D. Thesis, University of Chicago, 1995
    • S. Resnick, Dynamical problems in nonlinear advective partial differential equations. Ph.D. Thesis, University of Chicago, 1995
  • 11
    • 0002223508 scopus 로고    scopus 로고
    • On the critical dissipative quasigeostrophic equation
    • Constantin P., Cordoba D., and Wu J. On the critical dissipative quasigeostrophic equation. Indiana U. Math. J. 50 (2001) 97-107
    • (2001) Indiana U. Math. J. , vol.50 , pp. 97-107
    • Constantin, P.1    Cordoba, D.2    Wu, J.3
  • 12
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar
    • Constantin P., Majda A., and Tabak E. Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar. Nonlinearity 7 (1994) 1495-1533
    • (1994) Nonlinearity , vol.7 , pp. 1495-1533
    • Constantin, P.1    Majda, A.2    Tabak, E.3
  • 13
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
    • Bony J.-M. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Ecole Norm. Sup. 14 (1981) 209-246
    • (1981) Ann. Ecole Norm. Sup. , vol.14 , pp. 209-246
    • Bony, J.-M.1
  • 14
    • 47049131261 scopus 로고    scopus 로고
    • A. Cheskidov, P. Constantin, S. Friedlander, R. Shvydkoy, Energy conservation and Onsager's conjecture for the Euler equations. arXiv:Math.AP/0704.0759, 2007
    • A. Cheskidov, P. Constantin, S. Friedlander, R. Shvydkoy, Energy conservation and Onsager's conjecture for the Euler equations. arXiv:Math.AP/0704.0759, 2007
  • 15
    • 33846337789 scopus 로고    scopus 로고
    • Regularity of inviscid shell models of turbulence
    • Constantin P., Levant B., and Titi E. Regularity of inviscid shell models of turbulence. Phys. Rev. E 75 1 (2007) 016305
    • (2007) Phys. Rev. E , vol.75 , Issue.1 , pp. 016305
    • Constantin, P.1    Levant, B.2    Titi, E.3
  • 16
    • 47049111455 scopus 로고    scopus 로고
    • C. De Lellis, L. Szekelyhidi, The Euler equations as differential inclusions, 2007. Preprint
    • C. De Lellis, L. Szekelyhidi, The Euler equations as differential inclusions, 2007. Preprint
  • 17
    • 0031491102 scopus 로고    scopus 로고
    • On the nonuniqueness of weak solution of the Euler equation
    • Shnirelman A. On the nonuniqueness of weak solution of the Euler equation. Comm. Pure Appl. Math. 50 (1997) 1261-1286
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1261-1286
    • Shnirelman, A.1
  • 19
    • 0002205604 scopus 로고
    • Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer
    • Eyink G.L. Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer. Phys. D 78 (1994) 222-240
    • (1994) Phys. D , vol.78 , pp. 222-240
    • Eyink, G.L.1
  • 20
    • 21844522201 scopus 로고
    • Onsager's conjecture on the energy conservation for solutions of Euler's equation
    • Constantin P., and Titi W.E.E. Onsager's conjecture on the energy conservation for solutions of Euler's equation. Commun. Math. Phys. 165 (1994) 207-209
    • (1994) Commun. Math. Phys. , vol.165 , pp. 207-209
    • Constantin, P.1    Titi, W.E.E.2
  • 21
    • 0033630156 scopus 로고    scopus 로고
    • Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
    • Duchon J., and Robert R. Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations. Nonlinearity 13 (2000) 249-255
    • (2000) Nonlinearity , vol.13 , pp. 249-255
    • Duchon, J.1    Robert, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.