-
Previous Article
Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain
- DCDS Home
- This Issue
-
Next Article
Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system
Attractors for the three-dimensional incompressible Navier-Stokes equations with damping
1. | College of science, Xi’an Jiaotong University, Xi’an, 710049, China, China |
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[2] |
X. Cai and Q. Jiu, Weak and strong solutions for the incompressible Navier-Stokes equations with damping, J. Math. Anal. Appl., 343 (2008), 799-809.
doi: 10.1016/j.jmaa.2008.01.041. |
[3] |
A. Cheskidov and C. Foias, On global attractors of the 3D Navier-Stokes equations, J. Diff. Eqns., 231 (2006), 714-754.
doi: 10.1016/j.jde.2006.08.021. |
[4] |
N. J. Cutland, Global attractors for small samples and germs of 3D Navier-Stokes equations, Nonlinear Anal., 62 (2005), 265-281.
doi: 10.1016/j.na.2005.02.114. |
[5] |
A. V. Kapustyan and J. Valero, Weak and srong attractors for the 3D Navier-Stokes system, J. Diff. Eqns., 240 (2007), 249-278.
doi: 10.1016/j.jde.2007.06.008. |
[6] |
J. C. Robinson, "Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors," Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001. |
[7] |
R. Rosa, The global attractors for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Anal., 32 (1998), 71-85.
doi: 10.1016/S0362-546X(97)00453-7. |
[8] |
G. R. Sell, Global attractors for the three-dimensional Navier-Stokes equations, J. Dynamics Differential Equations, 8 (1996), 1-33.
doi: 10.1007/BF02218613. |
[9] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[10] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, Studies in Mathematics and its Applications, 2, North-Holland Publishing Co., Amsterdam, 1984. |
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[2] |
X. Cai and Q. Jiu, Weak and strong solutions for the incompressible Navier-Stokes equations with damping, J. Math. Anal. Appl., 343 (2008), 799-809.
doi: 10.1016/j.jmaa.2008.01.041. |
[3] |
A. Cheskidov and C. Foias, On global attractors of the 3D Navier-Stokes equations, J. Diff. Eqns., 231 (2006), 714-754.
doi: 10.1016/j.jde.2006.08.021. |
[4] |
N. J. Cutland, Global attractors for small samples and germs of 3D Navier-Stokes equations, Nonlinear Anal., 62 (2005), 265-281.
doi: 10.1016/j.na.2005.02.114. |
[5] |
A. V. Kapustyan and J. Valero, Weak and srong attractors for the 3D Navier-Stokes system, J. Diff. Eqns., 240 (2007), 249-278.
doi: 10.1016/j.jde.2007.06.008. |
[6] |
J. C. Robinson, "Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors," Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001. |
[7] |
R. Rosa, The global attractors for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Anal., 32 (1998), 71-85.
doi: 10.1016/S0362-546X(97)00453-7. |
[8] |
G. R. Sell, Global attractors for the three-dimensional Navier-Stokes equations, J. Dynamics Differential Equations, 8 (1996), 1-33.
doi: 10.1007/BF02218613. |
[9] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[10] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, Studies in Mathematics and its Applications, 2, North-Holland Publishing Co., Amsterdam, 1984. |
[1] |
Yongfu Wang. Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier-Stokes flows with vacuum. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4317-4333. doi: 10.3934/dcdsb.2020099 |
[2] |
Lihuai Du, Ting Zhang. Local and global strong solution to the stochastic 3-D incompressible anisotropic Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4745-4765. doi: 10.3934/dcds.2018209 |
[3] |
Xin Zhong. Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3563-3578. doi: 10.3934/dcdsb.2020246 |
[4] |
Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible Navier-Stokes. Kinetic and Related Models, 2016, 9 (1) : 75-103. doi: 10.3934/krm.2016.9.75 |
[5] |
Chérif Amrouche, María Ángeles Rodríguez-Bellido. On the very weak solution for the Oseen and Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 159-183. doi: 10.3934/dcdss.2010.3.159 |
[6] |
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6207-6228. doi: 10.3934/dcdsb.2021015 |
[7] |
Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5383-5405. doi: 10.3934/dcdsb.2020348 |
[8] |
Ciprian Foias, Ricardo Rosa, Roger Temam. Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1611-1631. doi: 10.3934/dcds.2010.27.1611 |
[9] |
Yong Yang, Bingsheng Zhang. On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:Ⅰ. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2339-2350. doi: 10.3934/dcdsb.2017101 |
[10] |
Daniel Pardo, José Valero, Ángel Giménez. Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3569-3590. doi: 10.3934/dcdsb.2018279 |
[11] |
Francesca Crispo, Paolo Maremonti. A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1283-1294. doi: 10.3934/dcds.2017053 |
[12] |
J. Huang, Marius Paicu. Decay estimates of global solution to 2D incompressible Navier-Stokes equations with variable viscosity. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4647-4669. doi: 10.3934/dcds.2014.34.4647 |
[13] |
Qi S. Zhang. An example of large global smooth solution of 3 dimensional Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5521-5523. doi: 10.3934/dcds.2013.33.5521 |
[14] |
Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133 |
[15] |
Wenjing Song, Ganshan Yang. The regularization of solution for the coupled Navier-Stokes and Maxwell equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2113-2127. doi: 10.3934/dcdss.2016087 |
[16] |
Atanas Stefanov. On the Lipschitzness of the solution map for the 2 D Navier-Stokes system. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1471-1490. doi: 10.3934/dcds.2010.26.1471 |
[17] |
Jingrui Wang, Keyan Wang. Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 5003-5019. doi: 10.3934/dcds.2017215 |
[18] |
Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1801-1816. doi: 10.3934/dcdsb.2017107 |
[19] |
Fang Li, Bo You, Yao Xu. Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4267-4284. doi: 10.3934/dcdsb.2018137 |
[20] |
Anis Dhifaoui. $ L^p $-strong solution for the stationary exterior Stokes equations with Navier boundary condition. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1403-1420. doi: 10.3934/dcdss.2022086 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]