The Estimation of the Hausdorff and Fractal Dimensions of the Global Attractor for 2D Autonomous g-Navier-Stokes Equations

Jin Ping Jiang; Xiao Xia Wang

doi:10.4028/www.scientific.net/AMM.511-512.1235

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 511-512The Estimation of the Hausdorff and Fractal...

The Estimation of the Hausdorff and Fractal Dimensions of the Global Attractor for 2D Autonomous g-Navier-Stokes Equations

Abstract:

In this paper, by using the energyequation method, the 2D g-Navier-Stokes equations with linear dampness on some unbounded domains wereinvestigated without the restriction of the forcing term belongingto some weighted Sobolev space. Moreover,the estimation of theHausdorff and Fractal dimensions of such attractors were alsoobtained.

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Periodical:

Applied Mechanics and Materials (Volumes 511-512)

Pages:

1235-1238

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.511-512.1235

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Online since:

February 2014

Authors:

Jin Ping Jiang*, Xiao Xia Wang

Keywords:

Global Attractor, g-Navier-Stokes Equations, Hausdorff and Fractal Dimensions, Linear Dampness

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References

[1] J. Roh, g-Navier-Stokes equations, Thesis, University of Minnesota, (2001).

Google Scholar

[2] J.K. Hale and G. Raugel, A damped hyperbolic equation on thin domains, Trans. amer. Math. Soc. 329 (1992)185-219.

DOI: 10.1090/s0002-9947-1992-1040261-1

Google Scholar

[3] R. Temam and M. Ziane, Navier-Stokes equations in three-dimensions thin domains with various boundary conditions, Adv. Differential Equations 1(1996), 499-546.

DOI: 10.57262/ade/1366896027

Google Scholar

[4] R. Temam,M. Ziane, Navier-Stokes equations in thin spherical domains, in: Contemp. Math. Vol. 209 (1997) 281-314.

DOI: 10.1090/conm/209/02772

Google Scholar

[5] G. Raugel and G.R. sell, Navier-Stokes equations on thin 3D domains,I. Global attractors and global regularity of solutions,J. Amer. Math. Soc. 6(1993), 503-568.

DOI: 10.1090/s0894-0347-1993-1179539-4

Google Scholar

[6] G. Raugel G.R. Sell, Navier-Stokes equations on thin 3D domains II, Global regularity of spa tially periodic solutions, in: Nonlinear Partial Differentical Equations and Their Applications, college de France Seminar, Longman, Harlow, XI(1994).

DOI: 10.2307/2152776

Google Scholar

[7] J. Roh, Dynamics of the g-Navier-stokes equations,J. differential Equations 211(2005) 452-484.

Google Scholar

[8] G.R. Sell,Y. You, Dynamics of Evolutionary Equations, Applied Mathematical Sciences, Vol. 143, Springer, New York, (2002).

Google Scholar

[9] H. Bae and J. Roh, Existence of solutions of the g-Navier-Stokes equations, Tai wanese J. Math, 8(1) (2004)85-102.

Google Scholar

[10] R. Temam, Navier-Stokes equations: theory and numerical analysis, Reprient of the 1984 edition, AMS Chelsea Publishing, Providence, RI, (2001).

Google Scholar