JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE GLOBAL ATTRACTOR OF THE 2D G-NAVIER-STOKES EQUATIONS ON SOME UNBOUNDED DOMAINS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE GLOBAL ATTRACTOR OF THE 2D G-NAVIER-STOKES EQUATIONS ON SOME UNBOUNDED DOMAINS
Kwean, Hyuk-Jin; Roh, Jai-Ok;
  PDF(new window)
 Abstract
In this paper, we study the two dimensional g-Navier­Stokes equations on some unbounded domain . We prove the existence of the global attractor for the two dimensional g-Navier­Stokes equations under suitable conditions. Also, we estimate the dimension of the global attractor. For this purpose, we exploit the concept of asymptotic compactness used by Rosa for the usual Navier-Stokes equations.
 Keywords
G-Navier-stokes equations;global attractor;Hausdorff and fractal dimensions;
 Language
English
 Cited by
1.
ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS,;

대한수학회논문집, 2014. vol.29. 4, pp.505-518 crossref(new window)
1.
PULLBACK ATTRACTORS FOR STRONG SOLUTIONS OF 2D NON-AUTONOMOUS g-NAVIER-STOKES EQUATIONS, Acta Mathematica Vietnamica, 2015, 40, 4, 637  crossref(new windwow)
2.
On the Stationary Solutions to 2D g-Navier-Stokes Equations, Acta Mathematica Vietnamica, 2016  crossref(new windwow)
3.
ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS, Communications of the Korean Mathematical Society, 2014, 29, 4, 505  crossref(new windwow)
4.
Existence and finite time approximation of strong solutions to 2D g-Navier–Stokes equations, Acta Mathematica Vietnamica, 2013, 38, 3, 413  crossref(new windwow)
5.
Spectral Galerkin Method in Space and Time for the 2Dg-Navier-Stokes Equations, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
6.
PULLBACK ATTRACTORS FOR 2D g-NAVIER-STOKES EQUATIONS WITH INFINITE DELAYS, Communications of the Korean Mathematical Society, 2016, 31, 3, 519  crossref(new windwow)
 References
1.
F. Abergel, Attractor for a Navier-Stokes flow in an unbounded domain, Math. Model. Anal. 23 (1989), no. 3, 359-370

2.
F. Abergel, Existence and finite dimensionality of the global aitractor for evolution equations on unbounded domains, J. Differential Equations 83 (1990), no. 1, 85-108 crossref(new window)

3.
A. V. Babin, The attractor of a Navier-Stokes system in an unbounded channellike domain, J. Dynam. Differential Equations 4 (1992), no. 4, 555-584 crossref(new window)

4.
A. V. Babin and M. I. Vishik, Attractors of partial differential equations in an unbounded domain, Proc. Roy. Soc. Edinburgh Sect. A 116A (1990), 221-243

5.
H. Bae and J. Roh, Existence of solutions of the g-Navier-Stokes equations, Taiwanese J. Math. 8 (2004), no. 1, 85-102

6.
P. Constantin and C. Foias, Global Lyapunov exponents, Kaplan-Yorke fomulas and the dimension of the attmctor for the 2D Navier-Stokes equations, Comm. Pure Appl. Math. XXXVIII (1985), 1-27

7.
P. Constantin, C. Foias, C. Manley, and R. Temam, Determining modes and fractal dimension of turbulent flows, J. Fluid Mech. 150 (1988), 427-440

8.
P. Constantin, C. Foias, and R. Temam, Attractor representing turbulent flows, Mem. Amer. Math. Soc. 53 (1985). no. 314

9.
C. Foias and R. Temam, Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures Appl, 58 (1979), 334-368

10.
J. K. Hale and G. Raugel, A damped hyperbolic equation on thin domains, Trans. Amer. Math. Soc. 329 (1992), 185-219 crossref(new window)

11.
D. Hundertmark, A. Laptev, and T. Weidl, New bounds on the Lieb-Thirring constants, Invent. Math. 140 (2000), no. 3, 693-704 crossref(new window)

12.
O. Ladyzhenskaya, On the dynamical system generated by the navier-Stokes equations, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. lnst. Steklov.(POMI) 27 (1972), 91-114

13.
O. Ladyzhenskaya, On the dynamical system genemted by the runner-Stokes equations, English tranlation in J. of Soviet Math. 3 (1975),458-479 crossref(new window)

14.
O. Ladyzhenskaya, Attractor for Semigroup and Evolution Equations, Lezioni Lincei, Cam-bridge University Press, 1991

15.
I. Moise, R. Temam, and M. Ziane, Asymptotic analysis of the Navier-Stokes equations in thin domains, Topol. Methods Nonlinear Anal. 10 (1997), 249.--282

16.
S. Montgomery-Smith, Global regularity of the Navier-Stokes equations on thin three dimensional domains with periodic boundary condtitions, Electron. J. Differential Equations 11 (1999), 1-19 crossref(new window)

17.
G. Raugel and G. R. Sell, Naoier-Stokes equations on thin 3D domains. I. Global attmctors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993), 503-568 crossref(new window)

18.
G. Raugel and G. R. Sell, Navier-Stokes equations on thin 3D domains II, Global regularity of spa-tially periodic solutions, in 'Nonlinear Partial Differential Equations and Their Applications', College de France Seminar, Longman, Harlow, XI (1994), 205-247

19.
J. Roh, g-Navier-Stokes equations, Thesis, University of Minnesota, 2001

20.
J. Roh, g-Navier-Stokes equations, Dynamics of the g-Navier-Stokes equations, J. Differential Equations 211 (2005), issue 2, 452-484 crossref(new window)

21.
R. Rosa, The global attmctor fro the 2D Navier-Stokes Flow in some unbounded domains, Nonlinear Analysis, Theory, Methods, and Applications 32 (1998), no. 1, 71-85

22.
G. R. Sell and Y. You, Dynamics of evolutionary equations, Applied Mathematical Sciences, 143, Springer-Verlag, New York, 2002

23.
R. Temam, Infinite-Dimensional Dynamical System in Mechanics and Physics, Applied Mathematical Sciences, 68, Springer-Verlag, New-York, 1988

24.
R. Temam, Navier-Stokes Equations Theory and Numerical Analysis, Elsevier Sci-ence Pubilshers B. V. New York. 1979

25.
R. Temam and M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996), 499-546

26.
R. Temam and M. Ziane, Navier-Stokes equations in thin spherical domains, Contemp. Math. 209 (1997), 281-314 crossref(new window)