On Diffusive 2D Fokker–Planck–Navier–Stokes Systems
Tóm tắt
Từ khóa
Tài liệu tham khảo
Arnold, A., Carrillo, J.A., Desvillettes, L., Dolbeault, J., Jüngel, A., Lederman, C., Markowich, P.A., Toscani, G., Villani, C.: Entropies and equilibria of many-particle systems: an essay on recent research. Monatsh. Math. 142(1–2), 35–43, 2004
Arnold , A., Carrillo , J.A., Klapproth , C.: Improved entropy decay estimates for the heat equation. J. Math. Anal. Appl. 343(1), 190–206, 2008
Barrett , J.W., Boyaval , S.: Existence and approximation of a (regularized) Oldroyd-B model. Math. Models Methods Appl. Sci. 21(9), 1783–1837, 2011
Barrett , J.W., Süli , E.: Existence of global weak solutions to some regularized kinetic models for dilute polymers. Multiscale Model. Simul. 6(2), 506–546, 2007
Barrett , J.W., Süli , E.: Existence and equilibration of global weak solutions to kinetic models for dilute polymers I: finitely extensible nonlinear bead-spring chains. Math. Models Methods Appl. Sci. 21(6), 1211–1289, 2011
Barrett , J.W., Süli , E.: Existence and equilibration of global weak solutions to kinetic models for dilute polymers II: Hookean-type models. Math. Models Methods Appl. Sci. 22(5), 1150024, 84, 2012
Barrett , J.W., Süli , E.: Existence of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers with variable density and viscosity. J. Differ. Equ. 253(12), 3610–3677, 2012
Barrett , J.W., Süli , E.: Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids. Nonlinear Anal. Real World Appl. 39, 362–395, 2018
Beale , J.T., Kato , T., Majda , A.: Remarks on the breakdown of smooth solutions for the $$3$$-D Euler equations. Commun. Math. Phys. 94(1), 61–66, 1984
Bhave , A.V., Armstrong , R.C., Brown , R.A.: Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions. J. Chem. Phys. 95(4), 2988–3000, 1991
Billingsley , P.: Probability and Measure. Wiley Series in Probability and StatisticsWiley, Hoboken, NJ 2012. Anniversary edition [of MR1324786], With a foreword by Steve Lalley and a brief biography of Billingsley by Steve Koppes.
Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids. Vol. 1, 2nd edn. Fluid Mechanics. 1987.
Bird, R.B., Armstrong, R.C., Hassager, O., Curtiss, C.: Dynamics of Polymeric Liquids-Volume 2: Kinetic Theory. 1987.
Bogachev, V.I., Krylov, N.V., Röckner, M., Shaposhnikov, S.V.: Fokker–Planck–Kolmogorov Equations, vol. 207. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI 2015
Brezis , H.: Functional Analysis. Sobolev Spaces and Partial Differential Equations Universitext. Springer, New York 2011
Brézis , H.M., Lieb , E.A.: A relation between pointwise convergence of functions and convergence of functionals. Proc. Am. Math. Soc. 88(3), 486–490, 1983
Cáceres , M.A.J., Carrillo , J.A., Dolbeault , J.: Nonlinear stability in $$L^p$$ for a confined system of charged particles. SIAM J. Math. Anal. 34(2), 478–494, 2002
Chemin , J.-Y., Masmoudi , N.: About lifespan of regular solutions of equations related to viscoelastic fluids. SIAM J. Math. Anal. 33(1), 84–112, 2001
Constantin , P.: Nonlinear Fokker–Planck Navier–Stokes systems. Commun. Math. Sci. 3(4), 531–544, 2005
Constantin, P.: Smoluchowski Navier–Stokes systems. In: Stochastic Analysis and Partial Differential Equations, volume 429 of Contempory Mathematics, pp. 85–109. American Mathematical Society, Providence, RI, 2007.
Constantin, P.: Remarks on complex fluid models. In: Mathematical Aspects of Fluid Mechanics, volume 402 of London Mathematical Society. Lecture Note Series., pp. 70–87. Cambridge University Press, Cambridge, 2012.
Constantin , P., Fefferman , C., Titi , E.S., Zarnescu , A.: Regularity of coupled two-dimensional nonlinear Fokker–Planck and Navier–Stokes systems. Commun. Math. Phys. 270(3), 789–811, 2007
Constantin , P., Kliegl , M.: Note on global regularity for two-dimensional Oldroyd-B fluids with diffusive stress. Arch. Ration. Mech. Anal. 206(3), 725–740, 2012
Constantin , P., Masmoudi , N.: Global well-posedness for a Smoluchowski equation coupled with Navier–Stokes equations in 2D. Commun. Math. Phys. 278(1), 179–191, 2008
Constantin , P., Seregin , G.: Global regularity of solutions of coupled Navier–Stokes equations and nonlinear Fokker–Planck equations. Discrete Contin. Dyn. Syst. 26(4), 1185–1196, 2010
Constantin, P., Seregin, G.: Hölder continuity of solutions of 2D Navier–Stokes equations with singular forcing. In: Nonlinear Partial Differential Equations and Related Topics, volume 229 of American Mathematical Society Translation Series 2, pp. 87–95. American Mathematical Society, Providence, RI, 2010.
Constantin , P., Sun , W.: Remarks on Oldroyd-B and related complex fluid models. Commun. Math. Sci. 10(1), 33–73, 2012
Constantin , P., Zlatoš , A.: On the high intensity limit of interacting corpora. Commun. Math. Sci. 8(1), 173–186, 2010
Degond , P., Lemou , M., Picasso , M.: Viscoelastic fluid models derived from kinetic equations for polymers. SIAM J. Appl. Math. 62(5), 1501–1519, 2002
Degond , P., Liu , H.: Kinetic models for polymers with inertial effects. Netw. Heterog. Media4(4), 625–647, 2009
Diestel , J., Uhl Jr., J.J.: Vector Measures. American Mathematical Society, Providence, RI 1977. [With a foreword by B. J. Pettis, Mathematical Surveys, No. 15.]
DiPerna , R.J., Lions , P.-L.: On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. (2)130(2), 321–366, 1989
Doi, M., Edwards, S.: The Theory of Polymer Dynamics, 1986.
Du , Q., Liu , C., Yu , P.: FENE dumbbell model and its several linear and nonlinear closure approximations. Multiscale Model. Simul. 4(3), 709–731, 2005
El-Kareh , A.W., Leal , L.G.: Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion. J. Nonnewton. Fluid Mech. 33(3), 257–287, 1989
Elgindi , T.M., Liu , J.: Global wellposedness to the generalized Oldroyd type models in $$\mathbb{R}^3$$. J. Differ. Equ. 259(5), 1958–1966, 2015
Elgindi , T.M., Rousset , F.: Global regularity for some Oldroyd-B type models. Commun. Pure Appl. Math. 68(11), 2005–2021, 2015
Fang , D., Zi , R.: Global solutions to the Oldroyd-B model with a class of large initial data. SIAM J. Math. Anal. 48(2), 1054–1084, 2016
Fernández-Cara , E., Guillén , F., Ortega , R.R.: Some theoretical results for viscoplastic and dilatant fluids with variable density. Nonlinear Anal. 28(6), 1079–1100, 1997
Fernández-Cara , E., Guillén , F., Ortega , R.R.: Some theoretical results concerning non-Newtonian fluids of the Oldroyd kind. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)26(1), 1–29, 1998
Fernández-Cara, E., Guillén, F., Ortega, R.R.: Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind. In: Handbook of Numerical Analysis, vol. VIII, pp. 543–661. North-Holland, Amsterdam, 2002.
Giesekus , H.: A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Nonnewton. Fluid Mech. 11(1–2), 69–109, 1982
Guillopé , C., Saut , J.-C.: Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. 15(9), 849–869, 1990
Guillopé , C., Saut , J.-C.: Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type. RAIRO Modél. Math. Anal. Numér. 24(3), 369–401, 1990
Hieber , M., Naito , Y., Shibata , Y.: Global existence results for Oldroyd-B fluids in exterior domains. J. Differ. Equ. 252(3), 2617–2629, 2012
Hu , X., Lin , F.: Global solutions of two-dimensional incompressible viscoelastic flows with discontinuous initial data. Commun. Pure Appl. Math. 69(2), 372–404, 2016
Infusino, M.: Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions. In: Stochastic and Infinite Dimensional Analysis. Trends Mathematics, pp. 161–194. Springer, Cham, 2016.
Jordan , R., Kinderlehrer , D., Otto , F.: The variational formulation of the Fokker–Planck equation. SIAM J. Math. Anal. 29(1), 1–17, 1998
Joseph, D.D.: Fluid Dynamics of Viscoelastic Liquids, vol. 84. Applied Mathematical Sciences. Springer, New York 1990
Jourdain , B., Le Bris , C., Lelièvre , T., Otto , F.: Long-time asymptotics of a multiscale model for polymeric fluid flows. Arch. Ration. Mech. Anal. 181(1), 97–148, 2006
Jourdain , B., Lelièvre , T., Le Bris , C.: Existence of solution for a micro-macro model of polymeric fluid: the FENE model. J. Funct. Anal. 209(1), 162–193, 2004
Jüngel, A.: Entropy Methods for Diffusive Partial Differential Equations. Springer Briefs in Mathematics. Springer, Cham, 2016
Kreml , O.R., Pokorný , M.: On the local strong solutions for the FENE dumbbell model. Discrete Contin. Dyn. Syst. Ser. S3(2), 311–324, 2010
Kupferman , R., Mangoubi , C., Titi , E.S.: A Beale–Kato–Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime. Commun. Math. Sci. 6(1), 235–256, 2008
Le Bris, C., Lelièvre, T.: Multiscale modelling of complex fluids: a mathematical initiation. In: Multiscale Modeling and Simulation in Science, volume 66 of Lecture Notes in Computer Science and Engineering, pp. 49–137. Springer, Berlin, 2009
Lei , Z., Liu , C., Zhou , Y.: Global solutions for incompressible viscoelastic fluids. Arch. Ration. Mech. Anal. 188(3), 371–398, 2008
Lei , Z., Masmoudi , N., Zhou , Y.: Remarks on the blowup criteria for Oldroyd models. J. Differ. Equ. 248(2), 328–341, 2010
Lei , Z., Zhou , Y.: Global existence of classical solutions for the two-dimensional Oldroyd model via the incompressible limit. SIAM J. Math. Anal. 37(3), 797–814, 2005
Lieb, E.H., Loss, M.: Analysis, volume 14 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI, 2001
Lin , F.-H., Liu , C., Zhang , P.: On hydrodynamics of viscoelastic fluids. Commun. Pure Appl. Math. 58(11), 1437–1471, 2005
Lin , F.-H., Liu , C., Zhang , P.: On a micro-macro model for polymeric fluids near equilibrium. Commun. Pure Appl. Math. 60(6), 838–866, 2007
Lions , P.L., Masmoudi , N.: Global solutions for some Oldroyd models of non-Newtonian flows. Chin. Ann. Math. Ser. B21(2), 131–146, 2000
Lions , P.-L., Masmoudi , N.: Global existence of weak solutions to some micro-macro models. C. R. Math. Acad. Sci. Paris345(1), 15–20, 2007
Masmoudi , N.: Well-posedness for the FENE dumbbell model of polymeric flows. Commun. Pure Appl. Math. 61(12), 1685–1714, 2008
Masmoudi , N.: Global existence of weak solutions to the FENE dumbbell model of polymeric flows. Invent. Math. 191(2), 427–500, 2013
Masmoudi , N., Zhang , P., Zhang , Z.: Global well-posedness for 2D polymeric fluid models and growth estimate. Phys. D237(10–12), 1663–1675, 2008
Monin, A.S., Yaglom, A.M.: Statistical Fluid Dynamics, vol. I and II, pp. 1–32. MIT Press, Cambridge, 1971
Oldroyd , J.G.: On the formulation of rheological equations of state. Proc. R. Soc. Lond. Ser. A. 200, 523–541, 1950
Öttinger , H.C.: Stochastic Processes in Polymeric Fluids. Springer, Berlin 1996. [Tools and examples for developing simulation algorithms.]
Otto , F., Tzavaras , A.E.: Continuity of velocity gradients in suspensions of rod-like molecules. Commun. Math. Phys. 277(3), 729–758, 2008
Peterlin , A.: Hydrodynamics of macromolecules in a velocity field with longitudinal gradient. J. Polym. Sci. Part C Polym. Lett. 4(4), 287–291, 1966
Renardy , M.: An existence theorem for model equations resulting from kinetic theories of polymer solutions. SIAM J. Math. Anal. 22(2), 313–327, 1991
Schieber , J.D.: Generalized Brownian configuration fields for Fokker–Planck equations including center-of-mass diffusion. J. Nonnewton. Fluid Mech. 135(2–3), 179–181, 2006
Thien , N.P., Tanner , R.I.: A new constitutive equation derived from network theory. J. Nonnewton. Fluid Mech. 2(4), 353–365, 1977
Thomases , B.: An analysis of the effect of stress diffusion on the dynamics of creeping viscoelastic flow. J. Nonnewton. Fluid Mech. 166(21–22), 1221–1228, 2011
Thomases, B., Shelley, M.: Emergence of singular structures in Oldroyd-B fluids. Phys. Fluids19(10), 103103, 2007
Weinan , E., Li , T., Zhang , P.: Well-posedness for the dumbbell model of polymeric fluids. Commun. Math. Phys. 248(2), 409–427, 2004
Zhang , H., Zhang , P.: Local existence for the FENE-dumbbell model of polymeric fluids. Arch. Ration. Mech. Anal. 181(2), 373–400, 2006