Volume 43 Issue 4
Apr.  2022
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WANG Xiaoxia. Uniform Asymptoticity of the Solution to the 2D g-Navier-Stokes Equation With Nonlinear Damping[J]. Applied Mathematics and Mechanics, 2022, 43(4): 416-423. doi: 10.21656/1000-0887.410398
Citation: WANG Xiaoxia. Uniform Asymptoticity of the Solution to the 2D g-Navier-Stokes Equation With Nonlinear Damping[J]. Applied Mathematics and Mechanics, 2022, 43(4): 416-423. doi: 10.21656/1000-0887.410398

Uniform Asymptoticity of the Solution to the 2D g-Navier-Stokes Equation With Nonlinear Damping

doi: 10.21656/1000-0887.410398
  • Received Date: 2020-12-31
  • Accepted Date: 2021-10-10
  • Rev Recd Date: 2021-10-10
  • Available Online: 2022-03-16
  • Publish Date: 2022-04-01
  • The uniform asymptoticity of the 2D g-Navier-Stokes equation with nonlinear damping in a bounded domain was studied. The existence of the uniform absorption set of the process family and the satisfaction of the uniform condition (C) were proved, and the uniform attractors of the 2D g-Navier-Stokes equation with nonlinear damping were obtained.

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  • [1]
    ROH J. g-Navier-Stokes equations[D]. PhD Thesis. University of Minnesota, 2001.
    [2]
    BAE H O, ROH J. Existence of solutions of the g-Navier-Stokes equations[J]. Taiwanese Journal of Mathematics, 2004, 8(1): 85-102.
    [3]
    ROH J. Dynamics of the g-Navier-Stokes equations[J]. Journal of Differential Equations, 2005, 211(2): 452-484. doi: 10.1016/j.jde.2004.08.016
    [4]
    KWAK M, KWEANA H, ROH J. The dimension of attractor of the 2D g-Navier-Stokes equations[J]. Journal of Mathematical Analysis and Applications, 2006, 315(2): 436-461. doi: 10.1016/j.jmaa.2005.04.050
    [5]
    JIANG J P, HOU Y R. The global attractor of g-Navier-Stokes equations with linear dampness on R2[J]. Applied Mathematics and Computation, 2009, 215(3): 1068-1076. doi: 10.1016/j.amc.2009.06.035
    [6]
    JIANG J P, WANG X X. Global attractor of 2D autonomous g-Navier-Stokes equations[J]. Applied Mathematics and Mechanics(English Edition), 2013, 34(3): 385-394. doi: 10.1007/s10483-013-1678-7
    [7]
    姜金平, 侯延仁. 有界区域上2D非自治g-Navier-Stokes方程的拉回吸引子[J]. 应用数学和力学, 2010, 31(6): 670-680. (JIANG Jinping, HOU Yanren. Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains[J]. Applied Mathematics and Mechanics, 2010, 31(6): 670-680.(in Chinese) doi: 10.1007/s10483-010-1304-x
    [8]
    姜金平, 侯延仁, 王小霞. 含线性阻尼的2D非自治g-Navier-Stokes方程的拉回吸引子[J]. 应用数学和力学, 2011, 32(2): 144-157. (JIANG Jinping, HOU Yanren, WANG Xiaoxia. Pullback attractor of 2D nonautonomous g-Navier-Stokes equations with linear dampness[J]. Applied Mathematics and Mechanics, 2011, 32(2): 144-157.(in Chinese)
    [9]
    JIANG J P, HOU Y R, WANG X X. The pullback asymptotic behavior of the solutions for 2D nonautonomous g-Navier-Stokes equations[J]. Advances in Applied Mathematics and Mechanics, 2012, 4(2): 223-237. doi: 10.4208/aamm.10-m1071
    [10]
    ANH C T, QUYET D T. Long-time behavior for 2D non-autonomous g-Navier-Stokes equations[J]. Annales Polonici Mathematici, 2012, 103(3): 277-302. doi: 10.4064/ap103-3-5
    [11]
    QUYET D T. Pullback attractors for strong solutions of 2D non-autonomous g-Navier-Stokes equations[J]. Acta Mathematica Vietnamica, 2015, 40: 637-651. doi: 10.1007/s40306-014-0073-0
    [12]
    ANH C T, THANH N V, TUAN N V. On the stability of solutions to stochastic 2D g-Navier-Stokes equations with finite delays[J]. Random Operators and Stochastic Equations, 2017, 25(4): 1-14.
    [13]
    FENG X L, YOU B. Random attractors for the two-dimensional stochastic g-Navier-Stokes equations[J]. Stochastics: an International Journal of Probability and Stochastic Processes, 2020, 92(4): 613-626. doi: 10.1080/17442508.2019.1642340
    [14]
    BRZEZNIAK Z, CARABALLO T, LANGA J A, et al. Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains[J]. Journal of Differential Equations, 2013, 255: 3897-3919. doi: 10.1016/j.jde.2013.07.043
    [15]
    BRZEZNIAK Z, LI Y. Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains[J]. Transactions of the American Mathematical Society, 2006, 358(12): 5587-5629. doi: 10.1090/S0002-9947-06-03923-7
    [16]
    SONG X L, HOU Y R. Uniform attractora for three-dimensional Navier-Stokes equations with nonlinear damping[J]. Journal of Mathematical Analysis and Applications, 2015, 422(1): 337-351. doi: 10.1016/j.jmaa.2014.08.044
    [17]
    MA S, ZHONG C K, SONG H T. Attractors for nonautonomous 2D Navier-Stokes equations with less regular symbols[J]. Nonlinear Analysis: Theory, Methods & Applications, 2009, 71(9): 4215-4222.
    [18]
    TEMAM R. Infnite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York: Springer-Verlag, 1997.
    [19]
    LU S S, WU H Q, ZHONG C K. Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces[J]. Discrete & Continuous Dynamical Systems, 2005, 13(3): 701-719.
    [20]
    CHESKIDOV A, LU S S. Uniform global attractors for the nonautonomous 3D Navier-Stokes equations[J]. Advances in Mathematics, 2014, 267(2): 277-306.
    [21]
    MA Q F, WANG S H, ZHONG C K. Necessary and sufficient conditions for the existence of global attractors for semigroup and applications[J]. Indiana University Mathematics Journal, 2002, 51(6): 1541-1570. doi: 10.1512/iumj.2002.51.2255
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