Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1415-1427.
Previous Articles Next Articles
Asymptotic Behavior for the Damped Boussinesq
Xiaojing Cai*(
),Yanjie Zhou
- School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048
-
Received:2020-07-21Online:2021-10-26Published:2021-10-08 -
Contact:Xiaojing Cai E-mail:caixj@th.btbu.edu.cn -
Supported by:the National Key Research and Development Project(2017YFC1500301);the Joint Key Project of the NSFC and the China Earthquake Administration(U1839206);the Research Foundation for Advanced Talents of Beijing Technology and Business University(19008020161)
CLC Number:
- O175.29
Cite this article
Xiaojing Cai,Yanjie Zhou. Asymptotic Behavior for the Damped Boussinesq[J].Acta mathematica scientia,Series A, 2021, 41(5): 1415-1427.
share this article
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] | Zhang Chunguo, Fu Yuzhi, Liu Yubiao. Stability and Optimality of 2-D Mindlin-Timoshenko Plate System [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1465-1491. |
| [2] | Liu Zhiqing, Fang Zhongbo. 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. |
| [3] | 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. |
| [4] | 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. |
| [5] | 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. |
| [6] | Lianhong Guo. Research on the Inviscid Limit for Boussinesq Equations [J]. Acta mathematica scientia,Series A, 2021, 41(1): 91-99. |
| [7] | Yuanfei Li,Zhiqing Li. Phragmén-Lindelöf Type Results for Transient Heat Conduction Equation with Nonlinear Boundary Conditions [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1248-1258. |
| [8] | Zhiyu Zhang,Feifei Song,Tongxing Li,Yuanhong Yu. Oscillation Criteria of Second Order Nonlinear Neutral Emden-Fowler Differential Equations with Damping [J]. Acta mathematica scientia,Series A, 2020, 40(4): 934-946. |
| [9] | Menglan Liao,Bin Guo. Asymptotic Stability of Weak Solutions to Wave Equation with Variable Exponents and Strong Damping Term [J]. Acta mathematica scientia,Series A, 2020, 40(1): 146-155. |
| [10] | Junyu Lin,Minglian Wan,Muhua Cao. Decay Estimates of the Global Solution for the Landau-Lifshitz-Gilbert Equation in Three Dimensions [J]. Acta mathematica scientia,Series A, 2019, 39(6): 1443-1455. |
| [11] | Dongyan Li,Yan Dong. Singularity and Decay of Solutions for a Degenerate Semilinear Elliptic Equation [J]. Acta mathematica scientia,Series A, 2019, 39(6): 1376-1380. |
| [12] | Hua Qiu,Changping Xie,Shaomei Fang. Remarks on Regularity Criteria for 3D Generalized MHD Equations and Boussinesq Equations [J]. Acta mathematica scientia,Series A, 2019, 39(2): 316-328. |
| [13] | Yijun He,Huaihong Gao,Hua Wang,Shunyong Li. A Note on Global Solution and Blow-Up for a Class of Pseudo p-Laplacian Evolution Equations with Logarithmic Nonlinearity [J]. Acta mathematica scientia,Series A, 2019, 39(1): 125-132. |
| [14] | Liu Gongwei, Diao Lin. On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay [J]. Acta mathematica scientia,Series A, 2018, 38(3): 527-542. |
| [15] | Feng Baowei, Su Keqin. Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rn [J]. Acta mathematica scientia,Series A, 2018, 38(1): 122-133. |
|