Some mathematical questions related to the MHD equations
Journal Article
·
· Commun. Pure Appl. Math.; (United States)
Some questions relating to the large time behavior of the solutions of MHD equations for a viscous incompressible resistive fluid are investigated. The physical system is briefly described and the functional setting of the equations, a flow in a bounded domain or in whole space with a space periodicity property in all directions. The main existence and uniqueness results for weak and strong solutions of the MHD equations are recalled. Regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular. The squeezing property of the trajectories are stated and it is shown that any functional invariant set for the MHD equations, and in particular any attractor, has a finite Haussdorf dimension. The flow is found to be totally determined for large dimensions by a finite number of parameters. 26 references.
- Research Organization:
- Institut National de Recherche en Informatique et en Automatique, Le Chesnay, Yvelines, France
- OSTI ID:
- 6434277
- Journal Information:
- Commun. Pure Appl. Math.; (United States), Journal Name: Commun. Pure Appl. Math.; (United States) Vol. 36; ISSN CPAMA
- Country of Publication:
- United States
- Language:
- English
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