Frontiers of Mathematics in China >
H4-Boundedness of pullback attractor for a 2D non-Newtonian fluid flow
Received date: 02 Jun 2012
Accepted date: 08 Oct 2012
Published date: 01 Dec 2013
Copyright
We prove the H4-boundedness of the pullback attractor for a twodimensional non-autonomous non-Newtonian fluid in bounded domains.
Key words: H4-Boundedness; non-Newtonian fluid; pullback attractor
Guowei LIU , Caidi ZHAO , Juan CAO . H4-Boundedness of pullback attractor for a 2D non-Newtonian fluid flow[J]. Frontiers of Mathematics in China, 2013 , 8(6) : 1377 -1390 . DOI: 10.1007/s11464-013-0250-9
1 |
Adams R A. Sobolev Spaces. New York: Academic Press, 1975, 6
|
2 |
Bae Hyeong-Ohk. Existence, regularity and decay rate of solutions of non-Newtonian flow. J Math Appl Anal, 1999, 231: 467-491
|
3 |
Bellout H, Bloom F, Nečas J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Comm Partial Differential Equations, 1994, 19: 1763-1803
|
4 |
Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel: Existence and uniqueness of solutions. Nonlinear Anal, 2000, 19: 1763-1803
|
5 |
Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel: Existence of a maximal compact attractor. Nonlinear Anal, 2001, 43: 743-766
|
6 |
Dong B, Chen Z. Time decay rates of non-Newtonian flows in
|
7 |
Dong B, Jiang W. On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows. Sci China Ser A: Math, 2008, 51: 925-934
|
8 |
Dong B, Li Y. Large time behavior to the system of incompressible non-Newtonian fluids in
|
9 |
Friedman A. Partial Differential Equations. New York: Holt Reinhart and Winston, 1969
|
10 |
García-Luengo J, Marín-Rubio P, Real J. H2-boundedness of the pullback attractors for non-autonomous 2D Navier-Stokes equations in bounded domains. Nonlinear Anal, 2011, 74: 4882-4887
|
11 |
García-Luengo J, Marín-Rubio P, Real J. Pullback attractors in V for non-autonomous 2D Navier-Stokes equations and their tempered behavior. J Differential Equations, 2012, 252: 4333-4356
|
12 |
Guo B, Guo C. The convergence of non-Newtonian fluids to Navier-Stokes equations. J Math Anal Appl, 2009, 357: 468-478
|
13 |
Guo B, Guo C. The convergence for non-Newtonian fluids to Navier-Stokes equations in 3D domain. Int J Dyn Syst Differ Equ, 2009, 2: 129-138
|
14 |
Guo B, Lin G, Shang Y. Dynamics of Non-Newtonian Fluid. Beijing: National Defence Industry Press, 2006 (in Chinese)
|
15 |
Guo B, Zhu P. Partial regularity of suitable weak solution to the system of the incompressible non-Newtonian fluids. J Differential Equations, 2002, 178: 281-297
|
16 |
Ladyzhenskaya O. The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach Science Press, 1987
|
17 |
Málek J, Nečas J, Rokyta M, Ru˙žička M. Weak and Measure-valued Solutions to Evolutionary PDEs. New York: Champman-Hall, 1996
|
18 |
Pokorný M. Cauchy problem for the non-Newtonian viscous incompressible fluids. Appl Math, 1996, 41: 169-201
|
19 |
Robinson J C. Infinite-Dimensional Dynamical System. Cambridge: Cambridge University Press, 2001
|
20 |
Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. 2nd ed. Berlin: Springer, 1997
|
21 |
Zhao C, Li Y. H2-compact attractor for a non-Newtonian system in two-dimensional unbound domains. Nonlinear Anal, 2004, 56: 1091-1103
|
22 |
Zhao C, Li Y. A note on the asymptotic smoothing effect of solutions to a non-Newtonian system in 2-D unbounded domains. Nonlinear Anal, 2005, 60: 475-483
|
23 |
Zhao C, Li Y, Zhou S. Regularity of trajectory attractor and upper semicontinuity of global attractor for a 2D non-Newtonian fluid. J Differential Equations, 2009, 247: 2331-2363
|
24 |
Zhao C, Liu G, Wang W. Smooth pullback attractors for a non-autonomous 2D non-Newtonian fluid and their tempered behaviors. J Math Fluid Mech (to appear),
|
25 |
Zhao C, Zhou S. L2-compact uniform attractors for a nonautonomous incompressible non-Newtonian fluid with locally uniform integrable external forces in distribution space. J Math Phys, 2007, 48: 032702-1-12
|
26 |
Zhao C, Zhou S. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J Differential Equations, 2007, 238: 394-425
|
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