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Volumn 5, Issue 4, 2007, Pages 909-916

New entropy estimates for Oldroyd-B and related models

Author keywords

A priori estimate; Conformation tensor; Entropy; FENE P; Oldroyd B

Indexed keywords


EID: 39049136069     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2007.v5.n4.a9     Document Type: Article
Times cited : (75)

References (30)
  • 1
    • 18844385711 scopus 로고    scopus 로고
    • Existence of global weak solutions for some polymeric flow models, Math
    • J.W. Barrett, C. Schwab and E. Suli, Existence of global weak solutions for some polymeric flow models, Math. Models and Methods in Applied Sciences, 15(6), 939-983, 2005.
    • (2005) Models and Methods in Applied Sciences , vol.15 , Issue.6 , pp. 939-983
    • Barrett, J.W.1    Schwab, C.2    Suli, E.3
  • 2
    • 39049139418 scopus 로고    scopus 로고
    • Existence of global weak solutions to kinetic models for dilute polymers
    • J.W. Barrett and E. Suli, Existence of global weak solutions to kinetic models for dilute polymers, Multiscale Model. Simul., 6(2), 506-546, 2007.
    • (2007) Multiscale Model. Simul , vol.6 , Issue.2 , pp. 506-546
    • Barrett, J.W.1    Suli, E.2
  • 4
    • 0019028529 scopus 로고    scopus 로고
    • R.B. Bird, P. J. Dotson and N. L. Johnson, Polymer solution rheology based on a finitely extensible bead-spring chain model, J. Non-Newtonian Fluid Mech., 7, 213-235, 1980. Errata: J. Non-Newtonian Fluid Mech., 8, 193, 1981.
    • R.B. Bird, P. J. Dotson and N. L. Johnson, Polymer solution rheology based on a finitely extensible bead-spring chain model, J. Non-Newtonian Fluid Mech., 7, 213-235, 1980. Errata: J. Non-Newtonian Fluid Mech., 8, 193, 1981.
  • 5
    • 39049153938 scopus 로고    scopus 로고
    • A finite element scheme which preserves the free energy inequality in the Oldroyd-B model
    • in preparation
    • S. Boyaval, T. Lelièvre and C. Mangoubi, A finite element scheme which preserves the free energy inequality in the Oldroyd-B model, in preparation, 2007.
    • (2007)
    • Boyaval, S.1    Lelièvre, T.2    Mangoubi, C.3
  • 6
    • 8844269488 scopus 로고    scopus 로고
    • Constitutive laws for the matrix-logarithm of the conformation tensor
    • R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech., 123, 281-285, 2004.
    • (2004) J. Non-Newtonian Fluid Mech , vol.123 , pp. 281-285
    • Fattal, R.1    Kupferman, R.2
  • 7
    • 15344339745 scopus 로고    scopus 로고
    • Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation
    • R. Fattal and R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newtonian Fluid Mech., 126, 23-37, 2005.
    • (2005) J. Non-Newtonian Fluid Mech , vol.126 , pp. 23-37
    • Fattal, R.1    Kupferman, R.2
  • 8
    • 4243123633 scopus 로고    scopus 로고
    • n (Part 4), Techniques of scientific computing (Part 4), Numerical methods of fluids (Part 2), chapter: Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind, Amsterdam: North Holland/Elsevier, 543-661, 2002.
    • n (Part 4), Techniques of scientific computing (Part 4), Numerical methods of fluids (Part 2), chapter: Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind, Amsterdam: North Holland/Elsevier, 543-661, 2002.
  • 9
    • 0000325280 scopus 로고
    • Existence results for the flow of viscoelastic fluids with a differential constitutive law
    • C. Guillopé and J.C. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law, Nonlinear Analysis: Theory, Methods & Appl., 15(9), 849-869, 1990.
    • (1990) Nonlinear Analysis: Theory, Methods & Appl , vol.15 , Issue.9 , pp. 849-869
    • Guillopé, C.1    Saut, J.C.2
  • 10
    • 0001415885 scopus 로고
    • Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
    • C. Guillopé and J.C. Saut, Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type, RAIRO Math. Model. Num. Anal., 24(3), 369-401, 1990.
    • (1990) RAIRO Math. Model. Num. Anal , vol.24 , Issue.3 , pp. 369-401
    • Guillopé, C.1    Saut, J.C.2
  • 12
    • 39049132531 scopus 로고    scopus 로고
    • B. Jourdain and T. Lelièvre, Convergence of a stochastic particle approximation of the stress tensor for the FENE-P model, 2004. CERMICS 2004-263 report.
    • B. Jourdain and T. Lelièvre, Convergence of a stochastic particle approximation of the stress tensor for the FENE-P model, 2004. CERMICS 2004-263 report.
  • 15
    • 0026853119 scopus 로고
    • Analysis of simple constituive equations for viscoelastic fluids
    • A.I. Leonov, Analysis of simple constituive equations for viscoelastic fluids, J. Non-Newton. Fluid Mech., 42(3), 323-350, 1992.
    • (1992) J. Non-Newton. Fluid Mech , vol.42 , Issue.3 , pp. 323-350
    • Leonov, A.I.1
  • 16
    • 2942679256 scopus 로고    scopus 로고
    • Local existence for the dumbbell model of polymeric fluids
    • T. Li, H. Zhang and P.W. Zhang, Local existence for the dumbbell model of polymeric fluids, Comm. Part. Diff. Eq., 29(5-6), 903-923, 2004.
    • (2004) Comm. Part. Diff. Eq , vol.29 , Issue.5-6 , pp. 903-923
    • Li, T.1    Zhang, H.2    Zhang, P.W.3
  • 17
    • 34248575233 scopus 로고    scopus 로고
    • Mathematical analysis of multi-scale models of complex fluids
    • T. Li and P.W. Zhang, Mathematical analysis of multi-scale models of complex fluids, Commun. Math. Sci., 5(1), 1-51, 2007.
    • (2007) Commun. Math. Sci , vol.5 , Issue.1 , pp. 1-51
    • Li, T.1    Zhang, P.W.2
  • 18
    • 27844607354 scopus 로고    scopus 로고
    • On hydrodynamics of viscoelastic fluids
    • F. Lin, C. Liu and P.W. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math., 58(11), 1437-1471, 2005.
    • (2005) Comm. Pure Appl. Math , vol.58 , Issue.11 , pp. 1437-1471
    • Lin, F.1    Liu, C.2    Zhang, P.W.3
  • 19
    • 34247498198 scopus 로고    scopus 로고
    • On a micro-macro model for polymeric fluids near equilibrium
    • F. Lin, C. Liu and P.W. Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math., 60(6), 838-866, 2007.
    • (2007) Comm. Pure Appl. Math , vol.60 , Issue.6 , pp. 838-866
    • Lin, F.1    Liu, C.2    Zhang, P.W.3
  • 20
    • 0034381125 scopus 로고    scopus 로고
    • Global solutions for some Oldroyd models of non-newtonian flows
    • Chin. Ann. Math
    • P.L. Lions and N. Masmoudi, Global solutions for some Oldroyd models of non-newtonian flows, Chin. Ann. Math., Ser. B, 21(2), 131-146, 2000.
    • (2000) Ser. B , vol.21 , Issue.2 , pp. 131-146
    • Lions, P.L.1    Masmoudi, N.2
  • 21
    • 34447298371 scopus 로고    scopus 로고
    • Global existence of weak solutions to micro-macro models
    • P.L. Lions and N. Masmoudi, Global existence of weak solutions to micro-macro models, C. R. Math. Acad. Sci., 345(1), 15-20, 2007.
    • (2007) C. R. Math. Acad. Sci , vol.345 , Issue.1 , pp. 15-20
    • Lions, P.L.1    Masmoudi, N.2
  • 22
    • 38049095852 scopus 로고    scopus 로고
    • Well posedness for the FENE dumbbell model of polymeric flows
    • Technical report, New York University, 2007. Preprint available at
    • N. Masmoudi, Well posedness for the FENE dumbbell model of polymeric flows, Technical report, New York University, 2007. Preprint available at http://wvw.math.nyu.edu/faculty/masmoudi/index.html.
    • Masmoudi, N.1
  • 25
    • 0001081344 scopus 로고
    • Hydrodynamics of macromolecules in a velocity field with longitudinal gradient
    • A. Peterlin, Hydrodynamics of macromolecules in a velocity field with longitudinal gradient, J. Polym. Sci. B, 4, 287-291, 1966.
    • (1966) J. Polym. Sci. B , vol.4 , pp. 287-291
    • Peterlin, A.1
  • 26
    • 0346957816 scopus 로고
    • Local existence of solutions of the Dirichlet initial-boundary value problem for incompressible hypoelastic materials
    • M. Renardy, Local existence of solutions of the Dirichlet initial-boundary value problem for incompressible hypoelastic materials, SIAM J. Math. Anal., 21(6), 1369-1385, 1990.
    • (1990) SIAM J. Math. Anal , vol.21 , Issue.6 , pp. 1369-1385
    • Renardy, M.1
  • 27
    • 0005228558 scopus 로고
    • An existence theorem for model equations resulting from kinetic theories of polymer solutions
    • M. Renardy, An existence theorem for model equations resulting from kinetic theories of polymer solutions, SIAM J. Math. Anal., 22, 313-327, 1991.
    • (1991) SIAM J. Math. Anal , vol.22 , pp. 313-327
    • Renardy, M.1
  • 28
    • 0011380281 scopus 로고    scopus 로고
    • Thermodynamics of viscoelastic fluids
    • P. Wapperom and M.A. Hulsen, Thermodynamics of viscoelastic fluids, J. Rheol., 42(5), 999-1019, 1998.
    • (1998) J. Rheol , vol.42 , Issue.5 , pp. 999-1019
    • Wapperom, P.1    Hulsen, M.A.2
  • 29
    • 33646894129 scopus 로고    scopus 로고
    • Local existence for the FENE-dumbbell model of polymeric fluids
    • H. Zhang and P.W. Zhang, Local existence for the FENE-dumbbell model of polymeric fluids, Archive for Rational Mechanics and Analysis, 2, 373-400, 2006.
    • (2006) Archive for Rational Mechanics and Analysis , vol.2 , pp. 373-400
    • Zhang, H.1    Zhang, P.W.2
  • 30
    • 39049125208 scopus 로고    scopus 로고
    • Global weak solutions for Hookean-dumbbell model of dilute polymers
    • preprint
    • L. Zhang, H. Zhang and P.W. Zhang, Global weak solutions for Hookean-dumbbell model of dilute polymers, preprint, 2007.
    • (2007)
    • Zhang, L.1    Zhang, H.2    Zhang, P.W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.