대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권4호
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  • Pages.505-518
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  • 2014
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS

  • Quyet, Dao Trong (Faculty of Information Technology Le Quy Don Technical University)
  • 투고 : 2014.02.28
  • 발행 : 2014.10.31
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초록

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

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참고문헌

  1. C. T. Anh and D. T. Quyet, Long-time behavior for 2D non-autonomous g-Navier- Stokes equations, Ann. Pol. Math. 103 (2012), no. 3, 277-302. https://doi.org/10.4064/ap103-3-5
  2. C. T. Anh, D. T. Quyet, and D. T. Tinh, Existence and finite time approximation of strong solutions to 2D g-Navier-Stokes equations, Acta Math. Vietnam. 38 (2013), no. 3, 413-428. https://doi.org/10.1007/s40306-013-0023-2
  3. H. Bae and J. Roh, Existence of solutions of the g-Navier-Stokes equations, Taiwanese J. Math. 8 (2004), no. 1, 85-102. https://doi.org/10.11650/twjm/1500558459
  4. J. Jiang and Y. Hou, The global attractor of g-Navier-Stokes equations with linear dampness on $R^{2}$, Appl. Math. Comp. 215 (2009), no. 3, 1068-1076. https://doi.org/10.1016/j.amc.2009.06.035
  5. J. Jiang and Y. Hou, Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains, App. Math. Mech. (English Ed.) 31 (2010), no. 6, 697-708. https://doi.org/10.1007/s10483-010-1304-x
  6. M. Kwak, H. Kwean, and J. Roh, The dimension of attractor of the 2D g-Navier-Stokes equations, J. Math. Anal. Appl. 315 (2006), no. 2, 436-461. https://doi.org/10.1016/j.jmaa.2005.04.050
  7. H. Kwean and J. Roh, The global attractor of the 2D g-Navier-Stokes equations on some unbounded domains, Commun. Korean Math. Soc. 20 (2005), no. 4, 731-749. https://doi.org/10.4134/CKMS.2005.20.4.731
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  10. J. Roh, Convergence of the g-Navier-Stokes equations, Taiwanese J. Math. 13 (2009), no. 1, 189-210. https://doi.org/10.11650/twjm/1500405278
  11. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, 2nd edition, Am- sterdam: North-Holland, 1979.
  12. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd edition, Philadelphia, 1995.
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  14. D. Wu, The finite-dimensional uniform attractors for the nonautonomous g-Navier- Stokes equations, J. Appl. Math. 2009 (2009), Art. ID 150420, 17 pp.

피인용 문헌

  1. PULLBACK ATTRACTORS FOR 2D g-NAVIER-STOKES EQUATIONS WITH INFINITE DELAYS vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150186
  2. On the Stationary Solutions to 2D g-Navier-Stokes Equations vol.42, pp.2, 2017, https://doi.org/10.1007/s40306-016-0180-1