메뉴 건너뛰기




Volumn 8, Issue 3, 2010, Pages 763-782

Refined long-time asymptotics for some polymeric fluid flow models

Author keywords

Dumbbell model; Entropy method; Exponential decay rate; Fokker Planck equations; Large time behavior; Polymeric flow; Relative entropy

Indexed keywords


EID: 77954652354     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2010.v8.n3.a8     Document Type: Article
Times cited : (19)

References (33)
  • 1
    • 77954654691 scopus 로고    scopus 로고
    • A generalized Bakry-Emery condition for non-symmetric diffusions
    • Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels (Eds.); World Scientific Publishing
    • A. Arnold and E. Carlen, A generalized Bakry-Emery condition for non-symmetric diffusions, in EQUADIFF 99 -Proceedings of the Internat. Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels (Eds.); World Scientific Publishing, 732-734, 2000.
    • (2000) EQUADIFF 99 -Proceedings of the Internat , pp. 732-734
    • Arnold, A.1    Carlen, E.2
  • 2
    • 77951203698 scopus 로고    scopus 로고
    • Large-time behavior of non-symmetric Fokker-Planck type equations
    • A. Arnold, E. Carlen and Q. Ju, Large-time behavior of non-symmetric Fokker-Planck type equations, Commun. Stochastic Anal., 2(1), 153-175, 2008.
    • (2008) Commun. Stochastic Anal. , vol.2 , Issue.1 , pp. 153-175
    • Arnold, A.1    Carlen, E.2    Ju, Q.3
  • 4
    • 0002042431 scopus 로고    scopus 로고
    • On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Plack type equations
    • A. Arnold, P. Markowich, G. Toscani and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Plack type equations, Commun. PDE, 26, 43-100, 2001.
    • (2001) Commun. PDE , vol.26 , pp. 43-100
    • Arnold, A.1    Markowich, P.2    Toscani, G.3    Unterreiter, A.4
  • 5
    • 0346777245 scopus 로고    scopus 로고
    • Entropy decay of discretized Fokker-Planck equations I temporal semi-discretization
    • A. Arnold and A. Unterreiter, Entropy decay of discretized Fokker-Planck equations I temporal semi-discretization, Comput. Math. Appl., 46(10-11), 1683-1690, 2003.
    • (2003) Comput. Math. Appl. , vol.46 , Issue.10-11 , pp. 1683-1690
    • Arnold, A.1    Unterreiter, A.2
  • 6
    • 0001362443 scopus 로고
    • Hypercontractivité de semi-groupes de diffusion, C.R
    • D. Bakry and M. Emery, Hypercontractivité de semi-groupes de diffusion, C.R. Acad. Sci. Paris Sér., I, 15, 299-305, 1984.
    • (1984) Acad. Sci. Paris Sér., I , vol.15 , pp. 299-305
    • Bakry, D.1    Emery, M.2
  • 7
    • 0001119849 scopus 로고
    • Sém. Prob. XIX, Lecture Notes in Math. Springer
    • D. Bakry and M. Emery, Diffusions hypercontractivities, Sém. Prob. XIX, Lecture Notes in Math. Springer, 1123, 177-206, 1985.
    • (1985) Diffusions hypercontractivities , vol.1123 , pp. 177-206
    • Bakry, D.1    Emery, M.2
  • 8
    • 84976855597 scopus 로고
    • Algorithm 432: solution of the matrix equation AX+XB=C, Commun
    • R.H. Bartels and G.W. Stewart, Algorithm 432: solution of the matrix equation AX+XB=C, Commun. ACM, 15, 820-826, 1972.
    • (1972) ACM , vol.15 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 12
    • 77954636665 scopus 로고    scopus 로고
    • The FENE model for viscoelastic thin film flows
    • L. Chupin, The FENE model for viscoelastic thin film flows, Methods and Appl. of Analysis, 16(1), 217-262, 2009.
    • (2009) Methods and Appl. of Analysis , vol.16 , Issue.1 , pp. 217-262
    • Chupin, L.1
  • 13
    • 0000489740 scopus 로고
    • Information-type measures of difference of probability distributions and indirect observations
    • I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Stud. Sci. Math. Hung., 2, 299-318, 1967.
    • (1967) Stud. Sci. Math. Hung. , vol.2 , pp. 299-318
    • Csiszár, I.1
  • 14
    • 0004074550 scopus 로고
    • International Series of Monographs on Physics, Oxford University Press, Oxford
    • M. Doi and S.F. Edwards, The Theory of Polymer Dynamics, International Series of Monographs on Physics, Oxford University Press, Oxford, 1988.
    • (1988) The Theory of Polymer Dynamics
    • Doi, M.1    Edwards, S.F.2
  • 15
    • 33646692641 scopus 로고    scopus 로고
    • FENE dumbbell model and its several linear and nonlinear closure approximations
    • Q. Du, C. Liu and P. Yu, FENE dumbbell model and its several linear and nonlinear closure approximations, Multiscale Model. Simul., 4, 709-731, 2005.
    • (2005) Multiscale Model. Simul. , vol.4 , pp. 709-731
    • Du, Q.1    Liu, C.2    Yu, P.3
  • 16
    • 0001359676 scopus 로고
    • Logarithmic Sobolev inequalities and stochastic Ising models
    • R. Holley and D. Stroock, Logarithmic Sobolev inequalities and stochastic Ising models, J. Stat. Phys., 46(5-6), 1159-1194, 1987.
    • (1987) J. Stat. Phys. , vol.46 , Issue.5-6 , pp. 1159-1194
    • Holley, R.1    Stroock, D.2
  • 18
    • 77954635593 scopus 로고    scopus 로고
    • A macroscopic closure approximation to the micromacro FENE models with maximum entropy principle for polymeric materials
    • Y. Hyon, J.A. Carrillo, Q. Du and C. Liu, A macroscopic closure approximation to the micromacro FENE models with maximum entropy principle for polymeric materials, Kinetic and Related Models, 2, 171-184, 2008.
    • (2008) Kinetic and Related Models , vol.2 , pp. 171-184
    • Hyon, Y.1    Carrillo, J.A.2    Du, Q.3    Liu, C.4
  • 19
    • 33646682174 scopus 로고    scopus 로고
    • Long-time asymptotics of a multiscale model for polymeric fluid flows
    • B. Jourdain, C. Le Bris, T. Lelièvre and F. Otto, Long-time asymptotics of a multiscale model for polymeric fluid flows, Arch. Rational Mech. Anal., 181, 97-148, 2006.
    • (2006) Arch. Rational Mech. Anal. , vol.181 , pp. 97-148
    • Jourdain, B.1    Le Bris, C.2    Lelièvre, T.3    Otto, F.4
  • 22
    • 21344489142 scopus 로고
    • An attainable lower bound for the best normal approximation
    • L. László, An attainable lower bound for the best normal approximation, SIAM J. Matrix Analysis and Applications, 15, 1035-1043, 1994.
    • (1994) SIAM J. Matrix Analysis and Applications , vol.15 , pp. 1035-1043
    • László, L.1
  • 23
    • 34247498198 scopus 로고    scopus 로고
    • On a micro-macro model for polymeric fluids near equilibrium
    • F. Lin, C. Liu and P. Zhang, On a micro-macro model for polymeric fluids near equilibrium, Commun. Pure Appl. Math., 60(6), 838-866, 2007.
    • (2007) Commun. Pure Appl. Math. , vol.60 , Issue.6 , pp. 838-866
    • Lin, F.1    Liu, C.2    Zhang, P.3
  • 24
    • 55149120747 scopus 로고    scopus 로고
    • Boundary conditions for the microscopic FENE models
    • C. Liu and H. Liu, Boundary conditions for the microscopic FENE models, SIAM J. Appl. Math., 68(5), 1304-1315, 2008.
    • (2008) SIAM J. Appl. Math. , vol.68 , Issue.5 , pp. 1304-1315
    • Liu, C.1    Liu, H.2
  • 26
    • 0038243436 scopus 로고    scopus 로고
    • On the trend to equilibrium for the Fokker-Plack equation: an interplay between physics and functional analysis
    • P.A. Markowich and C. Villani, On the trend to equilibrium for the Fokker-Plack equation: an interplay between physics and functional analysis, Mat. Contemp., 19, 1-29, 2000.
    • (2000) Mat. Contemp. , vol.19 , pp. 1-29
    • Markowich, P.A.1    Villani, C.2
  • 27
    • 55749083845 scopus 로고    scopus 로고
    • Well posedness for the FENE dumbbell model of polymeric flows
    • N. Masmoudi, Well posedness for the FENE dumbbell model of polymeric flows, CPAM, 61(12), 1685-1714, 2008.
    • (2008) CPAM , vol.61 , Issue.12 , pp. 1685-1714
    • Masmoudi, N.1
  • 30
    • 0000305146 scopus 로고
    • Closest normal matrix finally found!
    • A. Ruhe, Closest normal matrix finally found! BIT, 27, 585-598, 1987.
    • (1987) BIT , vol.27 , pp. 585-598
    • Ruhe, A.1
  • 31
    • 0012699568 scopus 로고
    • On nonnegative solutions of the equation AD+DA′ =-C
    • J. Snyders and M. Zakai, On nonnegative solutions of the equation AD+DA′ =-C, SIAM J. Appl. Math., 18, 704-714, 1970.
    • (1970) SIAM J. Appl. Math. , vol.18 , pp. 704-714
    • Snyders, J.1    Zakai, M.2
  • 32
    • 0003261335 scopus 로고
    • Interpolation Theory, Function Spaces
    • Barth Verlag, Heidelberg-Leipzig
    • H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Barth Verlag, Heidelberg-Leipzig, 1995.
    • (1995) Differential Operators
    • Triebel, H.1
  • 33
    • 33646894129 scopus 로고    scopus 로고
    • Local existence for the FENE-dumbbell model of polymeric fluids
    • H. Zhang and P. Zhang, Local existence for the FENE-dumbbell model of polymeric fluids, Arch. Ration. Mech. Anal., 181, 373-400, 2006.
    • (2006) Arch. Ration. Mech. Anal. , vol.181 , pp. 373-400
    • Zhang, H.1    Zhang, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.