含非线性阻尼的2D <i>g</i>-Navier-Stokes方程解的一致渐近性

王小霞

doi:10.21656/1000-0887.410398

含非线性阻尼的2D g-Navier-Stokes方程解的一致渐近性

doi: 10.21656/1000-0887.410398

王小霞

延安大学数学与计算机科学学院，陕西延安 716000

基金项目: 国家自然科学基金(11971378)；陕西省自然科学基金(2018JM1042)；陕西省大学生创新创业训练计划（S202110719115）

详细信息

作者简介:
王小霞（1978—），女，副教授，硕士，硕士生导师（E-mail：yd-wxx@163.com）

中图分类号: O175; O35
计量
- 文章访问数: 392
- HTML全文浏览量: 224
- PDF下载量: 44
- 被引次数: 0
出版历程
- 收稿日期: 2020-12-31
- 录用日期: 2021-10-10
- 修回日期: 2021-10-10
- 网络出版日期: 2022-03-16
- 刊出日期: 2022-04-01

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

WANG Xiaoxia

College of Mathematics and Computer Science, Yan’an University, Yan’an, Shaanxi 716000, P.R.China

摘要

摘要:
研究了有界区域上含非线性阻尼的2D g-Navier-Stokes 方程解的一致渐近性，通过证明过程族的一致吸收集存在和一致条件(C)成立，得到了含非线性阻尼的2D g-Navier-Stokes 方程一致吸引子存在。
- g-Navier-Stokes 方程 /
- 一致条件(C) /
- 一致渐近性
Abstract:
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.
- g-Navier-Stokes equation /
- uniform condition (C) /
- uniform asymptoticity

HTML全文

参考文献(21)

[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