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Volumn 38, Issue 1, 1998, Pages 1-19

On the two-dimensional Navier-Stokes equations with the free boundary condition

Author keywords

Elongated domains; Global attractors; Grashof number; Hausdorff and fractal dimensions; Navier Stokes equations; Trilinear form

Indexed keywords

BOUNDARY CONDITIONS; FRACTALS; TURBULENCE;

EID: 0032123966     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900079     Document Type: Article
Times cited : (14)

References (14)
  • 1
    • 84957122398 scopus 로고
    • Attractors of partial differential equations and estimate of their dimensions
    • A. V. Babin and M.I. Vishik, Attractors of partial differential equations and estimate of their dimensions, Russian Math. Survey 38 (1983), 151-213.
    • (1983) Russian Math. Survey , vol.38 , pp. 151-213
    • Babin, A.V.1    Vishik, M.I.2
  • 3
    • 0023999086 scopus 로고
    • On the dimension of the attractors in two-dimensional turbulence
    • P. Constantin, C. Foias, and R. Temam, On the dimension of the attractors in two-dimensional turbulence, Phys. D 30 (1988), 284-296.
    • (1988) Phys. D , vol.30 , pp. 284-296
    • Constantin, P.1    Foias, C.2    Temam, R.3
  • 4
    • 0020830393 scopus 로고
    • Asymptotic analysis of the Navier-Stokes equations
    • P. Constantin, C. Foias, R. Temam, and Y. Treve, Asymptotic analysis of the Navier-Stokes equations, Phys. D 9 (1983), 157-188.
    • (1983) Phys. D , vol.9 , pp. 157-188
    • Constantin, P.1    Foias, C.2    Temam, R.3    Treve, Y.4
  • 6
    • 11744284881 scopus 로고
    • Lower bound on the dimension of the attractor for the Navier-Stokes equations in space dimension 3
    • North-Holland Delta Ser., North-Holland, Amsterdam
    • J.M. Ghidaglia and R. Temam, Lower bound on the dimension of the attractor for the Navier-Stokes equations in space dimension 3, in Mechanics, Analysis and Geometry: 200 Years after Lagrange, North-Holland Delta Ser., North-Holland, Amsterdam, 1991.
    • (1991) Mechanics, Analysis and Geometry: 200 Years after Lagrange
    • Ghidaglia, J.M.1    Temam, R.2
  • 7
    • 84972521483 scopus 로고
    • Generalization of Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors
    • J.M. Ghidaglia, M. Marion, and R. Temam, Generalization of Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors, Differential Integral Equations 1 (1988), 1-21.
    • (1988) Differential Integral Equations , vol.1 , pp. 1-21
    • Ghidaglia, J.M.1    Marion, M.2    Temam, R.3
  • 8
    • 11744331310 scopus 로고
    • Lower bound on the dimension of the attractor for the Bénard problem with free surfaces
    • A. Miranville, Lower bound on the dimension of the attractor for the Bénard problem with free surfaces. Nonlinear Anal. 25 (1995), 1079-1094.
    • (1995) Nonlinear Anal. , vol.25 , pp. 1079-1094
    • Miranville, A.1
  • 9
    • 11744260767 scopus 로고    scopus 로고
    • On the dimension of the attractor for the Bénard problem with free surfaces
    • To appear
    • A. Miranville and M. Ziane, On the dimension of the attractor for the Bénard problem with free surfaces. To appear in Russian J. Math. Phys.
    • Russian J. Math. Phys.
    • Miranville, A.1    Ziane, M.2
  • 13
    • 0000502277 scopus 로고    scopus 로고
    • Navier-Stokes equations in three-dimensional thin domains with various boundary conditions
    • R. Temam and M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996), 499-546.
    • (1996) Adv. Differential Equations , vol.1 , pp. 499-546
    • Temam, R.1    Ziane, M.2
  • 14
    • 0002266080 scopus 로고    scopus 로고
    • Optimal bounds of the dimensions of the attractors of the Navier-Stokes equations
    • M. Ziane, Optimal bounds of the dimensions of the attractors of the Navier-Stokes equations, Phys. D 105 (1997), 1-19.
    • (1997) Phys. D , vol.105 , pp. 1-19
    • Ziane, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.