메뉴 건너뛰기




Volumn 6, Issue 2, 2004, Pages 157-168

Blow-up solutions appearing in the vorticity dynamics with linear strain

Author keywords

Blow up; Navier Stokes; Vorticity

Indexed keywords

DYNAMICS; INCOMPRESSIBLE FLOW; MAPPING; STRAIN; THEOREM PROVING;

EID: 4544333395     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-003-0087-1     Document Type: Article
Times cited : (6)

References (21)
  • 1
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • J. T. BEALE, T. KATO AND A. MAJDA, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66.
    • (1984) Comm. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 2
    • 84990576577 scopus 로고
    • Partial regularity of suitable weak solutions of the Navier-Stokes equations
    • L. CAFFARELLI, R. KOHN AND L. NIRENBERG, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 3
    • 23044524227 scopus 로고    scopus 로고
    • Global existence of solutions to the proudman-johnson equation
    • X. CHEN AND H. OKAMOTO, Global Existence of Solutions to the Proudman-Johnson Equation, Proc. Japan Acad. 76 (2000), 149-152.
    • (2000) Proc. Japan Acad. , vol.76 , pp. 149-152
    • Chen, X.1    Okamoto, H.2
  • 4
    • 0347998526 scopus 로고    scopus 로고
    • The euler equations and non-local conservative riccati equations
    • P. CONSTANTIN, The Euler equations and non-local conservative Riccati equations, Inter. Math. Res. Notice. 9 (2000), 455-465.
    • (2000) Inter. Math. Res. Notice , vol.9 , pp. 455-465
    • Constantin, P.1
  • 6
    • 4544349492 scopus 로고    scopus 로고
    • Nonlinear partial differential equations
    • in Japanese
    • Y. GIGA AND M.-H. GIGA, Nonlinear Partial Differential Equations, Kyoritsu Shuppan (1999) (in Japanese).
    • (1999) Kyoritsu Shuppan
    • Giga, Y.1    Giga, M.-H.2
  • 7
    • 0001226214 scopus 로고
    • Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation
    • Y. GIGA AND T. KAMBE, Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation, Commun. Math. Phys. 117 (1988), 549-568.
    • (1988) Commun. Math. Phys. , vol.117 , pp. 549-568
    • Giga, Y.1    Kambe, T.2
  • 8
    • 0031362111 scopus 로고    scopus 로고
    • Global blow-up of separable solutions of the vorticity equation
    • R. E. GRUNDY AND R. MCLAUGHLIN, Global blow-up of separable solutions of the vorticity equation, IMA J. Appl. Math. 59 (1997), 287-307.
    • (1997) IMA J. Appl. Math. , vol.59 , pp. 287-307
    • Grundy, R.E.1    Mclaughlin, R.2
  • 9
    • 0033345699 scopus 로고    scopus 로고
    • Three-dimensional blow-up solutions of the Navier-Stokes equations
    • R. E. GRUNDY AND R. MCLAUGHLIN, Three-dimensional blow-up solutions of the Navier-Stokes equations, IMA J. Appl. Math. 63 (1999), 287-306.
    • (1999) IMA J. Appl. Math. , vol.63 , pp. 287-306
    • Grundy, R.E.1    Mclaughlin, R.2
  • 11
    • 0034389838 scopus 로고    scopus 로고
    • Bilinear estimates in BMO and the Navier-Stokes equations
    • H. KOZONO AND Y. TANIUCHI, Bilinear estimates in BMO and the Navier-Stokes equations, Math. Z. 235 (2000), 173-194.
    • (2000) Math. Z. , vol.235 , pp. 173-194
    • Kozono, H.1    Taniuchi, Y.2
  • 13
    • 0344769882 scopus 로고
    • Strained spiral vortex model for turbulent fine structure
    • T. S. LUNDGREN, Strained spiral vortex model for turbulent fine structure, Phys. Fluid 25 (1982), 2193-2203.
    • (1982) Phys. Fluid , vol.25 , pp. 2193-2203
    • Lundgren, T.S.1
  • 15
    • 0003200409 scopus 로고    scopus 로고
    • Collapse of a class of three-dimensional euler vortices
    • S. J. A. MALHAM, Collapse of a class of three-dimensional Euler vortices, Proc. R. Soc. Lond. A 456 (2000), 2823-2833.
    • (2000) Proc. R. Soc. Lond. A , vol.456 , pp. 2823-2833
    • Malham, S.J.A.1
  • 16
    • 0033928092 scopus 로고    scopus 로고
    • The interaction of skewed vortex pairs: A model for blow-up of the Navier-Stokes equations
    • H. K. MOFFATT, The interaction of skewed vortex pairs: a model for blow-up of the Navier-Stokes equations, J. Fluid Mech. 409 (2000), 51-68.
    • (2000) J. Fluid Mech. , vol.409 , pp. 51-68
    • Moffatt, H.K.1
  • 17
    • 84893271162 scopus 로고    scopus 로고
    • On the blow-up of some similarity solutions of the Navier-Stokes equations
    • to appear
    • M. NAGAYAMA, H. OKAMOTO AND J. ZHU, On the blow-up of some similarity solutions of the Navier-Stokes equations, to appear in Quader, di Mat.
    • Quader. di Mat.
    • Nagayama, M.1    Okamoto, H.2    Zhu, J.3
  • 18
    • 4544324794 scopus 로고    scopus 로고
    • Blow-up problems modeled from the strain-vorticity dynamics
    • Proceedings of "Tosio Kato's Method and Principles for Evolution Equations in Mathematical Physics" (Eds. H. FUJITA, S. T. KURODA and H. OKAMOTO)
    • K. OHKITANI AND H. OKAMOTO, Blow-up problems modeled from the strain-vorticity dynamics, in: Proceedings of "Tosio Kato's Method and Principles for Evolution Equations in Mathematical Physics" (Eds. H. FUJITA, S. T. KURODA and H. OKAMOTO), RIMS Kokyuroku 1234 (2001), 240-250. Also at http://www.kurims.kyoto-u.ac.jp/~ okamoto/paper/paper.html
    • (2001) RIMS Kokyuroku , vol.1234 , pp. 240-250
    • Ohkitani, K.1    Okamoto, H.2
  • 19
    • 0034532989 scopus 로고    scopus 로고
    • Numerical study of singularity formation in a class of Euler and Navier-Stokes flows
    • K. OHKITANI AND J. D. GIBBON, Numerical study of singularity formation in a class of Euler and Navier-Stokes flows, Phys. Fluid 12 (2000), 3181-3194.
    • (2000) Phys. Fluid , vol.12 , pp. 3181-3194
    • Ohkitani, K.1    Gibbon, J.D.2
  • 21
    • 0002628126 scopus 로고    scopus 로고
    • Some similarity solutions of the Navier-Stokes equations and related topics
    • H. OKAMOTO AND J. ZHU, Some similarity solutions of the Navier-Stokes equations and related topics, Taiwanese J. Math. 4 (2000), 65-103.
    • (2000) Taiwanese J. Math. , vol.4 , pp. 65-103
    • Okamoto, H.1    Zhu, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.