메뉴 건너뛰기




Volumn 17, Issue 1, 2007, Pages 159-178

The global attractor for the solutions to the 3D viscous primitive equations

Author keywords

3D viscous primitive equations; Global attractor

Indexed keywords


EID: 33847752736     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2007.17.159     Document Type: Article
Times cited : (117)

References (41)
  • 1
    • 0001323666 scopus 로고
    • Un théorème de compacité
    • J. Aubin, Un théorème de compacité, C. R. Acad. Sci. Paris, 256 (1963), 5042-5044.
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 5042-5044
    • Aubin, J.1
  • 3
    • 0034383815 scopus 로고    scopus 로고
    • Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics
    • A. Babin, A. Mahalov and B. Nicolaenko, Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics, Math. Model. Numer. Anal. 34 (2000), 201-222.
    • (2000) Math. Model. Numer. Anal , vol.34 , pp. 201-222
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 4
    • 2142768721 scopus 로고    scopus 로고
    • Global attractors for semilinear wave equations
    • J. Ball, Global attractors for semilinear wave equations, Discr. Cont. Dyn. Sys. 10, (2004) 31-52.
    • (2004) Discr. Cont. Dyn. Sys , vol.10 , pp. 31-52
    • Ball, J.1
  • 5
    • 0001219545 scopus 로고
    • Existence of solutions to the Stommel-Charney model of the Gulf Stream
    • V. Barcilon, P. Constantin and E.S. Titi, Existence of solutions to the Stommel-Charney model of the Gulf Stream, SIAM J. Math. Anal. 19 (1988), 1355-1364.
    • (1988) SIAM J. Math. Anal , vol.19 , pp. 1355-1364
    • Barcilon, V.1    Constantin, P.2    Titi, E.S.3
  • 6
    • 8144227295 scopus 로고
    • Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean
    • A. Bourgeois, J. T. Beale, Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean, SIAM J. Math. Anal. 25 (1994), no. 4, 1023-1068.
    • (1994) SIAM J. Math. Anal , vol.25 , Issue.4 , pp. 1023-1068
    • Bourgeois, A.1    Beale, J.T.2
  • 7
    • 0037578614 scopus 로고    scopus 로고
    • Global well-posedness and finite dimensional global attractor for a 3-D planetary geostrophic viscous Model
    • C. Cao and E.S. Titi, Global well-posedness and finite dimensional global attractor for a 3-D planetary geostrophic viscous Model, Comm. Pure Appl. Math. 56, (2003), 198-233.
    • (2003) Comm. Pure Appl. Math , vol.56 , pp. 198-233
    • Cao, C.1    Titi, E.S.2
  • 8
    • 33847701147 scopus 로고    scopus 로고
    • C. Cao and E.S. Titi, Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics, arXiv: Math. AP/0503028 v2 16 Nov 2005.
    • C. Cao and E.S. Titi, Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics, arXiv: Math. AP/0503028 v2 16 Nov 2005.
  • 9
    • 4644247535 scopus 로고    scopus 로고
    • A "horizontal" hyper-diffusion 3-D thermocline planetary geostrophic model: Well-posedness and long time behavior
    • C. Cao, E.S. Titi and M. Ziane, A "horizontal" hyper-diffusion 3-D thermocline planetary geostrophic model: well-posedness and long time behavior, Nonlinearity 17, (2004), 1749-1776.
    • (2004) Nonlinearity , vol.17 , pp. 1749-1776
    • Cao, C.1    Titi, E.S.2    Ziane, M.3
  • 11
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
    • P. Constantin, A. Majda and E. Tabak, Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar, Nonlinearity, 7, (1994), 1495-1533.
    • (1994) Nonlinearity , vol.7 , pp. 1495-1533
    • Constantin, P.1    Majda, A.2    Tabak, E.3
  • 12
    • 0006748306 scopus 로고
    • Singular front formation in a model for quasigeostrophic flow
    • P. Constantin, A. Majda and E. Tabak, Singular front formation in a model for quasigeostrophic flow, Phys. Fluids, 6, (1994), 9-11.
    • (1994) Phys. Fluids , vol.6 , pp. 9-11
    • Constantin, P.1    Majda, A.2    Tabak, E.3
  • 13
    • 0040010955 scopus 로고    scopus 로고
    • Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers
    • P. Emid and A. Majda, Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers, Geophys. Astrophys. Fluid Dynam. 87 (1998), 1-50.
    • (1998) Geophys. Astrophys. Fluid Dynam , vol.87 , pp. 1-50
    • Emid, P.1    Majda, A.2
  • 14
    • 0002449201 scopus 로고
    • Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2
    • C. Foias and G. Prodi, Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2, Rend. Sem. Mat. Univ. Padova 39 (1967), 1-34.
    • (1967) Rend. Sem. Mat. Univ. Padova , vol.39 , pp. 1-34
    • Foias, C.1    Prodi, G.2
  • 15
    • 4944253479 scopus 로고    scopus 로고
    • Anisotropic estimates and strong solutions of the Primitive Equations
    • F. Guillén-Gonzáez, N. Masmoudi and M.A. Rodríguez-Bellido, Anisotropic estimates and strong solutions of the Primitive Equations, Diff. Integral Eq. 14(2001), no. 1, 1381-1408.
    • (2001) Diff. Integral Eq , vol.14 , Issue.1 , pp. 1381-1408
    • Guillén-Gonzáez, F.1    Masmoudi, N.2    Rodríguez-Bellido, M.A.3
  • 17
    • 0037259432 scopus 로고    scopus 로고
    • The primitive equations on the large scale ocean under the small depth hypothesis
    • C. Hu, R. Temam and M. Ziane, The primitive equations on the large scale ocean under the small depth hypothesis, Discrete Contin. Dyn. Syst. 9, (2003), 97-131.
    • (2003) Discrete Contin. Dyn. Syst , vol.9 , pp. 97-131
    • Hu, C.1    Temam, R.2    Ziane, M.3
  • 18
    • 0037050692 scopus 로고    scopus 로고
    • Mathematical analysis of geophysical balance models
    • D. Jones, Mathematical analysis of geophysical balance models, J. Diff. Eq. 179 (2002), 1-26.
    • (2002) J. Diff. Eq , vol.179 , pp. 1-26
    • Jones, D.1
  • 19
    • 0035402775 scopus 로고    scopus 로고
    • Existence of global attractor for the three-dimensional modified Navier-Stokes equations
    • N. Ju, Existence of global attractor for the three-dimensional modified Navier-Stokes equations, Nonlinearity, 14, (2001), no. 4, 777-786.
    • (2001) Nonlinearity , vol.14 , Issue.4 , pp. 777-786
    • Ju, N.1
  • 20
    • 33847701989 scopus 로고    scopus 로고
    • Dimensions of the global attractor for the 3D viscous primitive equations
    • in preparation
    • N. Ju, Dimensions of the global attractor for the 3D viscous primitive equations, in preparation.
    • Ju, N.1
  • 21
    • 33746280285 scopus 로고    scopus 로고
    • G. Kobelkov, Existence of a solution in whole for the large-scale ocean dynamics equations, 2006, Comptes Rendus Acad. Sci. Paris, to appear.
    • G. Kobelkov, Existence of a solution "in whole" for the large-scale ocean dynamics equations, 2006, Comptes Rendus Acad. Sci. Paris, to appear.
  • 23
    • 0028176865 scopus 로고
    • Attractors for the modifications of the three-dimensional Navier-Stokes equations
    • O. Ladyzhenskaya, Attractors for the modifications of the three-dimensional Navier-Stokes equations, Phil. Trans. R. Soc. A 346, (1994), 173-90.
    • (1994) Phil. Trans. R. Soc. A , vol.346 , pp. 173-190
    • Ladyzhenskaya, O.1
  • 26
    • 0000260611 scopus 로고
    • New formulations of the primitive equations of atmosphere and applications
    • J. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications, Nonlinearity 5, (1992), 237-288.
    • (1992) Nonlinearity , vol.5 , pp. 237-288
    • Lions, J.1    Temam, R.2    Wang, S.3
  • 27
    • 0001322085 scopus 로고
    • On the equations of the large scale Ocean
    • J. Lions, R. Temam and S. Wang, On the equations of the large scale Ocean, Nonlinearity 5, (1992), 1007-1053.
    • (1992) Nonlinearity , vol.5 , pp. 1007-1053
    • Lions, J.1    Temam, R.2    Wang, S.3
  • 28
    • 0000603572 scopus 로고
    • Mathematical theory for the coupled atmosphere-ocean models (CAO III)
    • J. Lions, R. Temam and S. Wang, Mathematical theory for the coupled atmosphere-ocean models (CAO III), J. Math. Pures Appl. 74, (1995), no. 2, 105-163.
    • (1995) J. Math. Pures Appl , vol.74 , Issue.2 , pp. 105-163
    • Lions, J.1    Temam, R.2    Wang, S.3
  • 29
    • 0036998040 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for the existence of global attractors for semigroups and applications
    • Q. Ma, S. Wang, C. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana Univ. Math. J. 51 (2002) 1541-1559.
    • (2002) Indiana Univ. Math. J , vol.51 , pp. 1541-1559
    • Ma, Q.1    Wang, S.2    Zhong, C.3
  • 30
    • 0004263512 scopus 로고    scopus 로고
    • Attractors for non-compact semigroups via energy equations
    • I. Moise, R. Rosa, X. Wang, Attractors for non-compact semigroups via energy equations, Nonlinearity, 11 (1998), no. 5, 1369-1393.
    • (1998) Nonlinearity , vol.11 , Issue.5 , pp. 1369-1393
    • Moise, I.1    Rosa, R.2    Wang, X.3
  • 34
    • 0008451717 scopus 로고    scopus 로고
    • Some mathematical properties of the planetary geostrophic equations for large scale ocean circulation
    • R. Samelson, R. Temam and S. Wang, Some mathematical properties of the planetary geostrophic equations for large scale ocean circulation, Applicable analysis, 70 (1998), 147-173.
    • (1998) Applicable analysis , vol.70 , pp. 147-173
    • Samelson, R.1    Temam, R.2    Wang, S.3
  • 35
    • 0008468989 scopus 로고    scopus 로고
    • Remarks on the planetary geostrophic model of gyre scale ocean circulation
    • R. Samelson, R. Temam and S. Wang, Remarks on the planetary geostrophic model of gyre scale ocean circulation, Differential and Integral Equation, 13 (2000), 1-14.
    • (2000) Differential and Integral Equation , vol.13 , pp. 1-14
    • Samelson, R.1    Temam, R.2    Wang, S.3
  • 39
    • 33847705196 scopus 로고    scopus 로고
    • Some mathematical aspects of geophysical fluid dynamics equations
    • R. Temam, Some mathematical aspects of geophysical fluid dynamics equations, Milan J. Math. 71, (2003), 175-198.
    • (2003) Milan J. Math , vol.71 , pp. 175-198
    • Temam, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.