Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress

We prove global regularity of solutions of Oldroyd-B equations in two spatial dimensions with spatial diffusion of the polymeric stresses.

[1]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

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

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

[4]  Hans Christian Öttinger,et al.  Stochastic Processes in Polymeric Fluids , 1996 .

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

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

[7]  Peter Constantin,et al.  Nonlinear Fokker-Planck Navier-Stokes systems , 2005 .

[8]  Yi Zhou,et al.  Global Existence of Classical Solutions for the Two-Dimensional Oldroyd Model via the Incompressible Limit , 2005, SIAM J. Math. Anal..

[9]  Ping Zhang,et al.  On hydrodynamics of viscoelastic fluids , 2005 .

[10]  Michael Shelley,et al.  Emergence of singular structures in Oldroyd-B fluids , 2007 .

[11]  Charles Fefferman,et al.  Regularity of Coupled Two-Dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems , 2006, math/0605245.

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

[13]  Ping Zhang,et al.  On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model , 2007 .

[14]  Ping Zhang,et al.  On a micro‐macro model for polymeric fluids near equilibrium , 2007 .

[15]  Pierre-Louis Lions,et al.  Global existence of weak solutions to some micro-macro models , 2007 .

[16]  E. Titi,et al.  A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime , 2007, 0709.1455.

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

[18]  Nader Masmoudi,et al.  Global Well-Posedness for a Smoluchowski Equation Coupled with Navier-Stokes Equations in 2D , 2008 .

[19]  Ping Zhang,et al.  Global well-posedness for 2D polymeric fluid models and growth estimate , 2008 .

[20]  Felix Otto,et al.  Continuity of Velocity Gradients in Suspensions of Rod–like Molecules , 2008 .

[21]  Peter Constantin,et al.  The Onsager equation for corpora , 2008, 0803.4326.

[22]  Claude Le Bris,et al.  Multiscale Modelling of Complex Fluids: A Mathematical Initiation , 2009 .

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

[24]  P. Constantin,et al.  Holder Continuity of Solutions of 2D Navier-Stokes Equations with Singular Forcing , 2009, 0901.3508.

[25]  Olof Runborg,et al.  Multiscale Modeling and Simulation in Science , 2009 .

[26]  P. Constantin,et al.  Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations , 2009, 0901.4462.

[27]  Nader Masmoudi,et al.  Global existence of weak solutions to the FENE dumbbell model of polymeric flows , 2010, Inventiones mathematicae.

[28]  John W. Barrett,et al.  Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers , 2010, 1004.1432.

[29]  Peter Constantin,et al.  On the high intensity limit of interacting corpora , 2010 .

[30]  Alexander I. Nazarov,et al.  Nonlinear Partial Differential Equations and Related Topics: Dedicated to Nina N. Uraltseva , 2010 .

[31]  Weiran Sun,et al.  Remarks on Oldroyd-B and Related Complex Fluids Models , 2010, 1009.0249.

[32]  B. Thomases.  An analysis of the effect of stress diffusion on the dynamics of creeping viscoelastic flow , 2011 .

[33]  John W. Barrett,et al.  Existence and equilibration of global weak solutions to kinetic models for dilute polymers I: finitely extensible nonlinear bead-spring chains , 2011 .

[34]  N. Masmoudi.  Global existence of weak solutions to macroscopic models of polymeric flows , 2011 .

[35]  E. Süli,et al.  Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers , 2012 .