Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1415-1427.
Previous Articles Next Articles
Received:
2020-07-21
Online:
2021-10-26
Published:
2021-10-08
Contact:
Xiaojing Cai
E-mail:caixj@th.btbu.edu.cn
Supported by:
CLC Number:
Xiaojing Cai,Yanjie Zhou. Asymptotic Behavior for the Damped Boussinesq[J].Acta mathematica scientia,Series A, 2021, 41(5): 1415-1427.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
1 | Bresch D , Desjardins B . Existence of global weak solution for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model. Comm Mech Phys, 2003, 238 (1/2): 211- 223 |
2 | Bresch D , Desjardins B , Lin Chi-Kun . On some compressible fluid models: Korteweg, lubricatior and shallow water systems. Comm Partial Diff Equa, 2003, 28 (3/4): 843- 868 |
3 |
Cai X , Jiu Q . Weak and strong solutions for the incompressible Navier-Stokes equations with damping. J Math Anal Appl, 2008, 343 (2): 799- 809
doi: 10.1016/j.jmaa.2008.01.041 |
4 |
Ye Z . Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms. Colloq Math, 2015, 139, 185- 203
doi: 10.4064/cm139-2-3 |
5 | Cai X , Lei L . L2 decay of the incompressible Navier-Stokes equations with damping. Acta Math Sci, 2010, 30B (4): 1235- 1248 |
6 |
Schonbek M E . L2 decay for weak solutions of the Navier-Stokes equations. Arch Ration Mech Anal, 1985, 88, 209- 222
doi: 10.1007/BF00752111 |
7 |
Schonbek M E . Lower bounds of rates of decay for solutions to the Navier-Stokes equations. J Amer Math Soc, 1991, 4 (3): 423- 449
doi: 10.1090/S0894-0347-1991-1103459-2 |
8 | Zhang L H . Sharp rate of decay of solutions to 2-dimensional Navierr-Stokes equations. Comm Partial Diff Equa, 1995, 20 (1/2): 119- 127 |
9 |
Zhou Y . A remark on the decay of solutions to the 3-D Navier-Stokes equations. Math Methods Appl Sci, 2007, 30 (10): 1223- 1229
doi: 10.1002/mma.841 |
10 |
Jia Y , Zhang X , Dong B . The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping. Nonlinear Anal: RWA, 2011, 12, 1736- 1747
doi: 10.1016/j.nonrwa.2010.11.006 |
11 |
Zhou Y . Regularity and uniqueness for the 3D incompressible Navier-Stokes equations with damping. Appl Math Lett, 2012, 25, 1822- 1825
doi: 10.1016/j.aml.2012.02.029 |
12 |
Zhang Z , Wu X , Lu M . On the uniqueness of strong solutions to the incompressible Navier-Stokes equations with damping. J Math Anal Appl, 2011, 377, 414- 419
doi: 10.1016/j.jmaa.2010.11.019 |
13 |
Jiang Z , Zhu M . The large time behavior of solutions to 3D Navier-Stokes equations with nonlinear damping. Math Mech Appl Sci, 2012, 35, 97- 102
doi: 10.1002/mma.1540 |
14 | Caffarelli L , Kohn R , Nirenberg L . Partial regularity of suitably weak solutions of the Navier-Stokes equations. Comm on Pure and Applied Math, 1982, 25, 771- 831 |
15 |
Leray J . Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math, 1934, 63, 193- 248
doi: 10.1007/BF02547354 |
16 |
Schonbek M E , Schonbek T P , Süli E . Large time behavier of solution to the Magneto-Hydrodynamics equations. Math Ann, 1996, 304, 717- 756
doi: 10.1007/BF01446316 |
17 |
Morimoto H . On non-stationary Boussinesq equations. Proc Japan Acad Ser A, 1991, 67, 159- 161
doi: 10.2183/pjab.67.159 |
18 | Morimoto H . On the existence and uniqueness of the stationary solution to the equation of natural convection. Tokyo J Math, 1991, 14, 217- 226 |
[1] | Zhu Weipeng, Li Jinlu, Wu Xing. Global Smooth Solutions of the Damped Boussinesq Equations with a Class of Large Initial Data [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1077-1085. |
[2] | Liu Anqi,Yu Ting,Xiang Changlin. Research on the Regularity of a Class of Biharmonic Map-Type Partial Differential Equation Systems [J]. Acta mathematica scientia,Series A, 2025, 45(2): 408-417. |
[3] | Liu Hui,Lin Lin,Sun Chengfeng. Global Strong Solution of 3D Temperature-Dependent Incompressible MHD-Boussinesq Equations with Fractional Dissipation [J]. Acta mathematica scientia,Series A, 2025, 45(2): 418-433. |
[4] | Yu Ting, Dong Ying. The Convergence Rate of the Fast Signal Diffusion Limit for a Three-Dimensional Keller-Segel-Stokes System [J]. Acta mathematica scientia,Series A, 2024, 44(4): 925-945. |
[5] | Han Zhongjie, He Yiheng, Zhao Zhixue. Indirect Stabilization and Optimal Decay Rates of Weakly Coupled Plates with Various Types of Damping [J]. Acta mathematica scientia,Series A, 2023, 43(6): 1681-1698. |
[6] | Chen Fei,Wang Shuai,Zhao Yongye,Wang Chuanbao. Time Decay Rate for Large-Solution About 3D Compressible MHD Equations [J]. Acta mathematica scientia,Series A, 2023, 43(5): 1397-1408. |
[7] | Li Xiaoli,Chen Xiaoli. Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation [J]. Acta mathematica scientia,Series A, 2023, 43(3): 754-770. |
[8] | Zaiyun Zhang,Zhenhai Liu,Youjun Deng. Global Existence and General Decay for a Nonlinear Viscoelastic Equation with Time-Varying Delay and Velocity-Dependent Material Density [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1684-1704. |
[9] | Baoyan Sun. Optimal Exponential Decay for the Linear Inhomogeneous Boltzmann Equation with Hard Potentials [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1853-1863. |
[10] | Chunguo Zhang,Yuzhi Fu,Yubiao Liu. Stability and Optimality of 2-D Mindlin-Timoshenko Plate System [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1465-1491. |
[11] | Zhiqing Liu,Zhongbo Fang. General Decay for the Transmission Problem of Viscoelastic Waves with not Necessarily Decreasing Kernel [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1428-1444. |
[12] | Yuanfei Li,Jincheng Shi,Huishan Zhu,Shiqi Huang. Fast Growth or Decay Estimates of Thermoelastic Equations in an External Domain [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1042-1052. |
[13] | Qianqian Xie,Xiaoping Zhai,Boqing Dong. Optimal Decay for the N-Dimensional Incompressible Oldroyd-B Model Without Damping Mechanism [J]. Acta mathematica scientia,Series A, 2021, 41(3): 762-769. |
[14] | Qing Chen. Optimal Time Decay Rate of the Highest Derivative of Solutions to the Compressible Navier-Stokes Equations [J]. Acta mathematica scientia,Series A, 2021, 41(2): 345-356. |
[15] | Lianhong Guo. Research on the Inviscid Limit for Boussinesq Equations [J]. Acta mathematica scientia,Series A, 2021, 41(1): 91-99. |
|