May  2004, 4(2): 465-478. doi: 10.3934/dcdsb.2004.4.465

The long-time evolution of mean field magnetohydrodynamics


Departamento de Análisis Matemático, Universidad de Valladolid, 47005 Valladolid, Spain

Received  October 2002 Revised  September 2003 Published  February 2004

The equations of mean field magnetohydrodynamics with constant mean velocity are proved to posses solutions bounded in the $H^{1}$-norm for all time, and a compact attractor whose dimension is estimated. It is shown that depending on the functional form of the so-called alpha term the attractor may reduce to zero or be a larger set. If, as usual in physical situations, there exists a set of solutions with a minimum size $N$, the dimension of this set decreases rapidly with increasing $N$. Finally, the dependence of the dimension on the magnetic diffusivity is analyzed, suggesting that the evolution of a magnetic field under the mean field equation is much more restricted than the one deduced from the full magnetohydrodynamic system.
Citation: Manuel Núñez. The long-time evolution of mean field magnetohydrodynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 465-478. doi: 10.3934/dcdsb.2004.4.465

Jie Li, Xiangdong Ye, Tao Yu. Mean equicontinuity, complexity and applications. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 359-393. doi: 10.3934/dcds.2020167


Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020345


Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073


João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138


Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018


Annegret Glitzky, Matthias Liero, Grigor Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020460


Dan Zhu, Rosemary A. Renaut, Hongwei Li, Tianyou Liu. Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020076


Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276

2019 Impact Factor: 1.27


  • PDF downloads (35)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]