[1] E W N, Li T J, Zhang P W. Well-posedness for the dumbbell model of polymeric fluids. Comm Math Phys, 2004, 248:409-427
[2] Gurtin M E. An Introduction to Continuum Mechanics. New York:Academic Press, 1981
[3] Larson R G. The Structure and Rheology of Complex Fluids. New York:Oxford University Press, 1995
[4] Liu C, Walkington N G. An Eulerian description of fluids containing viscohyperelastic particles. Arch Rational Mech Anal, 2001, 159:229-252
[5] Lin F H, Liu C, Zhang P. On hydrodynamics of viscoelastic fluids. Commun Pure Appl Math, 2005, 58:1437-1471
[6] Lei Z, Zhou Y. Global existence of classical solutions for 2D Oldroyd model via the incompressible limit. SIAM J Math Anal, 2005, 37:797-814
[7] Lei Z, Liu C, Zhou Y. Global solutions for incompressible viscoelastic fluids. Arch Rational Mech Anal, 2008, 188:371-398
[8] Lin F H, Zhang P. On the initial-boundary value problem of the incompressible viscoelastic fluid system. Commun Pure Appl Math, 2008, 61:539-558
[9] Chemin J Y, Masmoudi N. About lifespan of regular solutions of equations related to viscoelastic fluids. SIAM J Math Anal, 2001, 33:84-112
[10] Fan J S, Ozawa T. Regularity criterion for the incompressible viscoelastic fluid system. Houston J Math, 2011, 37:627-636
[11] He L B, Xu L. Global well-posedness for viscoelastic fluid system in bounded domains. SIAM J Math Anal, 2010, 42:2610-2625
[12] Lei Z. Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions. Discrete Contin Dyn Syst, 2014, 34:2861-2871
[13] Lei Z, Masmoudi N, Zhou Y. Remarks on the blowup criteria for Oldroyd models. J Differential Equations, 2010, 248:328-341
[14] Qian J Z. Well-posedness in critical spaces for incompressible viscoelastic fluid system. Nonlinear Anal, 2010, 72:3222-3234
[15] Zhang T, Fang D Y. Global well-posedness for the incompressible viscoelastic fluids in the critical L^p framework. SIAM J Math Anal, 2012, 44:2266-2288
[16] Cheskidov A, Holm D D, Olson E, et al. On a Leray-α model of turbulence. Proc R Soc Lond Ser A Math Phys Eng Sci, 2005, 461:629-649
[17] Chen S, Foias C, Holm D D, et al. Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys Rev Lett, 1988, 81:5338-5341
[18] Chen S, Foias C, Holm D D, et al. The Camassa-Holm equations and turbulence. Physica D, 1999, 133:49-65
[19] Foias C, Holm D D, Titi E S. The Navier-Stokes-alpha model of fluid turbulence. Physica D, 2001, 152:505-519
[20] Foias C, Holm D D, Titi E S. The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J Dyn Differ Equ, 2002, 14:1-35
[21] Ilyin A A, Lunasin E M, Titi E S. A Modified-Leray-α subgrid scale model of turbulence. Nonlinearity, 2006, 19:879-897
[22] Marsden J E, Shkoller S. Global well-posedness for the LANS-α equations on bounded domains. Proc Roy Soc Lon, 2001, 359:1449-1468
[23] Marsden J E, Shkoller S. The anisotropic Lagrangian averaged Euler and Navier-Stokes equations. Arch Rational Mech Anal, 2003, 166:27-46
[24] Mohseni K, Kosovi B, Shkoller S, et al. Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence. Phys Fluids, 2003, 15:524-544
[25] Kato T, Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Commun Pure Appl Math, 1988, 41:891-907
[26] Brezis H, Gallouet T. Nonlinear Schrödinger evolution equations. Nonlinear Anal, 1980, 4:677-681
[27] Brezis H, S. Wainger. A note on limiting cases of Sobolev embedding and convolution inequalities. Comm Partial Differential Equations, 1980, 5:773-789
[28] Coifman R, Lions P L, Meyer Y, et al. Compensated compactness and Hardy spaces. J Math Pures Appl, 1993, 72:247-286
[29] Catania D. Global existence for a regularized magnetohydrodynamic-α model. Ann Univ Ferrara, 2010, 56:1-20 |