|
|
H4-Boundedness of pullback attractor for a 2D non-Newtonian fluid flow |
Guowei LIU1, Caidi ZHAO1(), Juan CAO2 |
1. Department of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China; 2. College of Teacher Education, Wenzhou University, Wenzhou 325035, China |
|
|
Abstract We prove the H4-boundedness of the pullback attractor for a twodimensional non-autonomous non-Newtonian fluid in bounded domains.
|
Keywords
H4-Boundedness
non-Newtonian fluid
pullback attractor
|
Corresponding Author(s):
ZHAO Caidi,Email:zhaocaidi@yahoo.com.cn
|
Issue Date: 01 December 2013
|
|
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 doi: 10.1006/jmaa.1998.6242
|
3 |
Bellout H, Bloom F, Ne?as J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Comm Partial Differential Equations , 1994, 19: 1763-1803 doi: 10.1080/03605309408821073
|
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 doi: 10.1016/S0362-546X(99)00232-1
|
6 |
Dong B, Chen Z. Time decay rates of non-Newtonian flows in ?n+. J Math Anal Appl , 2006, 324: 820-833 doi: 10.1016/j.jmaa.2005.12.070
|
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 doi: 10.1007/s11425-007-0196-z
|
8 |
Dong B, Li Y. Large time behavior to the system of incompressible non-Newtonian fluids in ?2. J Math Anal Appl , 2004, 298: 667-676 doi: 10.1016/j.jmaa.2004.05.032
|
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 doi: 10.1016/j.na.2011.04.063
|
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 doi: 10.1016/j.jde.2012.01.010
|
12 |
Guo B, Guo C. The convergence of non-Newtonian fluids to Navier-Stokes equations. J Math Anal Appl , 2009, 357: 468-478 doi: 10.1016/j.jmaa.2009.04.027
|
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 doi: 10.1006/jdeq.2000.3958
|
16 |
Ladyzhenskaya O. The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach Science Press, 1987
|
17 |
Málek J, Ne?as J, Rokyta M, Ru˙?i?ka M. Weak and Measure-valued Solutions to Evolutionary PDEs. New York: Champman-Hall, 1996
|
18 |
Pokorny 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 doi: 10.1007/978-94-010-0732-0
|
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 doi: 10.1016/j.na.2003.11.006
|
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 doi: 10.1016/j.jde.2009.07.031
|
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) , pmid:10.1007/s00021-013-0153-2" target="blank"> doi: 10.1007/s00021-013-0153-2 pmid:10.1007/s00021-013-0153-2" target="blank"> doi: 10.1007/s00021-013-0153-2
|
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 doi: 10.1063/1.2709845
|
26 |
Zhao C, Zhou S. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J Differential Equations , 2007, 238: 394-425 doi: 10.1016/j.jde.2007.04.001
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|