American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations
  • DCDS Home
  • This Issue
  • Next Article
    Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential
January  2007, 17(1): 159-179. doi: 10.3934/dcds.2007.17.159

The global attractor for the solutions to the 3D viscous primitive equations

Ning Ju 1,

1. 

Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, United States

Received  March 2006 Revised  August 2006 Published  October 2006

Existence of the global attractor is proved for the strong solutions to the 3D viscous Primitive Equations (PEs) modeling large scale ocean and atmosphere dynamics. This result is obtained under the natural assumption that the external heat source $Q$ is square integrable. Furthermore, it is shown in [20] that the fractal and Hausdroff dimensions of the global attractor for 3D viscous PEs are both finite.
Keywords: 3D viscous Primitive Equations, global attractor..
Mathematics Subject Classification: 35B41, 35Q35, 37L, 65M70, 86A1.
Citation: Ning Ju. The global attractor for the solutions to the 3D viscous primitive equations. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 159-179. doi: 10.3934/dcds.2007.17.159
[1]

Ning Ju. The finite dimensional global attractor for the 3D viscous Primitive Equations. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 7001-7020. doi: 10.3934/dcds.2016104
[2]

Boling Guo, Guoli Zhou. Finite dimensionality of global attractor for the solutions to 3D viscous primitive equations of large-scale moist atmosphere. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4305-4327. doi: 10.3934/dcdsb.2018160
[3]

T. Tachim Medjo. Non-autonomous 3D primitive equations with oscillating external force and its global attractor. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 265-291. doi: 10.3934/dcds.2012.32.265
[4]

Makram Hamouda, Chang-Yeol Jung, Roger Temam. Asymptotic analysis for the 3D primitive equations in a channel. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 401-422. doi: 10.3934/dcdss.2013.6.401
[5]

Yuan Pei. Continuous data assimilation for the 3D primitive equations of the ocean. Communications on Pure and Applied Analysis, 2019, 18 (2) : 643-661. doi: 10.3934/cpaa.2019032
[6]

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
[7]

Xiaojie Yang, Hui Liu, Chengfeng Sun. Global attractors of the 3D micropolar equations with damping term. Mathematical Foundations of Computing, 2021, 4 (2) : 117-130. doi: 10.3934/mfc.2021007
[8]

Donatella Donatelli, Nóra Juhász. The primitive equations of the polluted atmosphere as a weak and strong limit of the 3D Navier-Stokes equations in downwind-matching coordinates. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2859-2892. doi: 10.3934/dcds.2022002
[9]

Xiuqing Wang, Yuming Qin, Alain Miranville. Approximation of the trajectory attractor of the 3D smectic-A liquid crystal flow equations. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3805-3827. doi: 10.3934/cpaa.2020168
[10]

Kush Kinra, Manil T. Mohan. Convergence of random attractors towards deterministic singleton attractor for 2D and 3D convective Brinkman-Forchheimer equations. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021061
[11]

T. Tachim Medjo. A non-autonomous 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external force and its global attractor. Communications on Pure and Applied Analysis, 2011, 10 (2) : 415-433. doi: 10.3934/cpaa.2011.10.415
[12]

Gabriel Deugoue. Approximation of the trajectory attractor of the 3D MHD System. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2119-2144. doi: 10.3934/cpaa.2013.12.2119
[13]

M. Bulíček, F. Ettwein, P. Kaplický, Dalibor Pražák. The dimension of the attractor for the 3D flow of a non-Newtonian fluid. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1503-1520. doi: 10.3934/cpaa.2009.8.1503
[14]

Yong Zhou. Remarks on regularities for the 3D MHD equations. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 881-886. doi: 10.3934/dcds.2005.12.881
[15]

Hyeong-Ohk Bae, Bum Ja Jin. Estimates of the wake for the 3D Oseen equations. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 1-18. doi: 10.3934/dcdsb.2008.10.1
[16]

Manil T. Mohan. Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3393-3436. doi: 10.3934/dcdsb.2020067
[17]

Jishan Fan, Fucai Li, Gen Nakamura. Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain. Conference Publications, 2015, 2015 (special) : 387-394. doi: 10.3934/proc.2015.0387
[18]

Yingdan Ji, Wen Tan. Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3271-3278. doi: 10.3934/dcdsb.2020227
[19]

Michael Röckner, Rongchan Zhu, Xiangchan Zhu. A remark on global solutions to random 3D vorticity equations for small initial data. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4021-4030. doi: 10.3934/dcdsb.2019048
[20]

Zhuan Ye. Remark on exponential decay-in-time of global strong solutions to 3D inhomogeneous incompressible micropolar equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6725-6743. doi: 10.3934/dcdsb.2019164

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (197)
  • HTML views (0)
  • Cited by (60)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy