Global Strong Solutions for Some Differential Viscoelastic Models

The purpose of this article is to show that there are many differential viscoelastic models for which the global existence of a regular solution is possible. Although the problem of global existenc...

[1]  P. Lions,et al.  GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS , 2000 .

[2]  Yoshikazu Giga,et al.  Abstract LP estimates for the Cauchy problem with applications to the Navier‐Stokes equations in exterior domains , 1991 .

[3]  Nader Masmoudi,et al.  Well‐posedness for the FENE dumbbell model of polymeric flows , 2008 .

[4]  R. Keunings,et al.  Numerical simulation of branched polymer melts in transient complex flow using pom-pom models , 2001 .

[5]  E. Fernández-Cara,et al.  Some theoretical results concerning non newtonian fluids of the Oldroyd kind , 1998 .

[6]  E. Mitsoulis.  50 Years of the K-BKZ Constitutive Relation for Polymers , 2013 .

[7]  Benjamin Jourdain,et al.  Existence of solution for a micro–macro model of polymeric fluid: the FENE model , 2004 .

[8]  M. F. Webster,et al.  Simulation of pressure‐tooling wire‐coating flow with Phan‐Thien/Tanner models , 2002 .

[9]  G. Fredrickson.  The theory of polymer dynamics , 1996 .

[10]  M.A. Hulsen.  A sufficient condition for a positive definite configuration tensor in differential models , 1990 .

[11]  Laurent Chupin,et al.  Global Existence Results for Some Viscoelastic Models with an Integral Constitutive Law , 2013, SIAM J. Math. Anal..

[12]  J. M. Rallison,et al.  Creeping flow of dilute polymer solutions past cylinders and spheres , 1988 .

[13]  J. Saut,et al.  Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type , 1990 .

[14]  E. Süli,et al.  Existence of global weak solutions for some polymeric flow models , 2005 .

[15]  E. Süli,et al.  EXISTENCE OF GLOBAL WEAK SOLUTIONS TO DUMBBELL MODELS FOR DILUTE POLYMERS WITH MICROSCOPIC CUT-OFF , 2008 .

[16]  A. Leonov.  Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids , 1994 .

[17]  M. Renardy,et al.  A singular perturbation study of the Rolie-Poly model , 2017, Journal of Non-Newtonian Fluid Mechanics.

[18]  Michael Renardy.  Existence of slow steady flows of viscoelastic fluids of integral type , 1988 .

[19]  L. Chupin.  Existence Results for the Flow of Viscoelastic Fluids with an Integral Constitutive Law , 2013 .

[20]  F. Baaijens,et al.  Viscoelastic analysis of complex polymer melt flows using the extended Pom-Pom model , 2002 .

[21]  F. Baaijens,et al.  Differential constitutive equations for polymer melts: The extended Pom–Pom model , 2001 .

[22]  Curtiss,et al.  Dynamics of Polymeric Liquids , .

[23]  H. Ch. Öttinger,et al.  Stochastic Processes in Polymeric Fluids: Tools and Examples for Developing Simulation Algorithms , 1995 .

[24]  B. Bernstein,et al.  A Study of Stress Relaxation with Finite Strain , 1963 .

[25]  R. Larson,et al.  Molecular constitutive equations for a class of branched polymers: The pom-pom polymer , 1998 .

[26]  J. Hadamard.  Sur les problemes aux derive espartielles et leur signification physique , 1902 .

[27]  R. Tanner,et al.  A new constitutive equation derived from network theory , 1977 .

[28]  Peter Constantin.  Smoluchowski Navier-Stokes Systems , 2007 .

[29]  Nader Masmoudi,et al.  Remarks on the blowup criteria for Oldroyd models , 2009, 0907.2745.

[30]  M. Renardy,et al.  A model equation for viscoelasticity with a strongly singular kernel , 1988 .

[31]  A Blowup Criterion for Ideal Viscoelastic Flow , 2011, 1102.1113.

[32]  C. L. Tucker,et al.  Fundamentals of Computer Modeling for Polymer Processing , 1989 .

[33]  R. Larson.  Constitutive equations for polymer melts and solutions , 1988 .

[34]  R. Larson.  A Constitutive Equation for Polymer Melts Based on Partially Extending Strand Convection , 1984 .

[35]  M. Crochet,et al.  Further Results On the Flow of a Viscoelastic Fluid Through An Abrupt Contraction , 1986 .

[36]  Raanan Fattal,et al.  Constitutive laws for the matrix-logarithm of the conformation tensor , 2004 .

[37]  A. R. Davies.  Reentrant corner singularities in non-newtonian flow. Part I: theory , 1988 .

[38]  R. Larson.  The elastic stress in “film fluids” , 1997 .

[39]  Pingwen Zhang,et al.  Local Existence for the FENE-Dumbbell Model of Polymeric Fluids , 2004 .

[40]  Raphaël Danchin,et al.  Density-Dependent Incompressible Fluids in Bounded Domains , 2006 .

[41]  Global Existence of Solutions for Shear Flow of Certain Viscoelastic Fluids , 2009 .

[42]  Michael Renardy,et al.  An existence theorem for model equations resulting from kinetic theories of polymer solutions , 1991 .

[43]  J. Saut,et al.  Existence results for the flow of viscoelastic fluids with a differential constitutive law , 1990 .

[44]  Guillén Fernández-Cara,et al.  GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE FENE DUMBBELL MODEL OF POLYMERIC FLOWS , 2012 .

[45]  Tony Lelièvre,et al.  Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics , 2011, 1102.0325.

[46]  Mária Lukácová-Medvid'ová,et al.  Global Existence Result for the Generalized Peterlin Viscoelastic Model , 2017, SIAM J. Math. Anal..

[47]  R. Keunings.  On the high weissenberg number problem , 1986 .

[48]  Enrique Fernández-Cara,et al.  EXISTENCE ET UNICITE DE SOLUTION FORTE LOCALE EN TEMPS POUR DES FLUIDES NON NEWTONIENS DE TYPE OLDROYD (VERSION LS-LT) , 1994 .

[49]  Jean-Yves Chemin,et al.  About Lifespan of Regular Solutions of Equations Related to Viscoelastic Fluids , 2001, SIAM J. Math. Anal..

[50]  N. Phan-Thien.  A Nonlinear Network Viscoelastic Model , 1978 .

[51]  T. Lelièvre,et al.  FREE-ENERGY-DISSIPATIVE SCHEMES FOR THE OLDROYD-B MODEL , 2008, 0801.2248.

[52]  J. Barrett,et al.  Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids , 2017, 1702.06502.

[53]  John W. Barrett,et al.  EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS II: HOOKEAN-TYPE MODELS , 2012 .

[54]  F. Greco,et al.  Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements , 2001 .

[55]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.