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ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS

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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 dimen- sional approximation of the strong solutions.

Abstract

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 dimen- sional approximation of the strong solutions.

참고문헌 (14)

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  2. C. T. Anh, "Existence and finite time approximation of strong solutions to 2D g-Navier-Stokes equations", Acta Math. Vietnam, 38(3), pp.413~428 (2013)
  3. H. Bae, "Existence of solutions of the g-Navier-Stokes equations", Taiwanese J. Math, 8(1), pp.85~102 (2004)
  4. J. Jiang, "The global attractor of g-Navier-Stokes equations with linear dampness on R²", Appl. Math. Comp, 215(3), pp.1068~1076 (2009)
  5. J. Jiang, "Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains", App. Math. Mech. (English Ed.), 31(6), pp.697~708 (2010)
  6. M. Kwak, "The dimension of attractor of", J. Math. Anal. Appl, 315(2), pp.436~461 (2006)
  7. 권혁진, "The Global Attractor of the 2D g-Navier-Stokes Equations on some unbounded domains", 대한수학회논문집, 20(4), pp.731~749 (2005), 대한수학회
  8. J. Roh, "Dynamics of the g-Navier-Stokes equations", J. Differential Equations, 211(2), pp.452~484 (2005)
  9. 노재옥, "Derivation of the $g$-Navier-Stokes equations", 충청수학회지, 19(3), pp.213~218 (2006), 충청수학회
  10. J. Roh, "Convergence of the g-Navier-Stokes equations", Taiwanese J. Math, 13(1), pp.189~210 (2009)
  11. R. Temam, "Navier-Stokes Equations: Theory and Numerical Analysis" (1979), North-Holland
  12. R. Temam, "Navier-Stokes Equations and Nonlinear Functional Analysis" (1995), Philadelphia
  13. R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics" (1997), Springer-Verlag
  14. D. Wu, "The finite-dimensional uniform attractors for the nonautonomous g-Navier-Stokes equations", J. Appl. Math, 2009, pp.17~ (2009)

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