Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion

We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity...

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Bibliographic Details
Published in:Communications in partial differential equations 2007-11, Vol.32 (11), p.1791-1812
Main Authors: Agapito, Rubén, Schonbek, Maria
Format: Article
Language:English
Subjects:
Decay rates
Magneto-hydrodynamics
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Summary:We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity of the velocity is enough to prevent such oscillations. When magnetic diffusion is present and the data is only in L 2 , it is shown that the solutions decay to zero without a rate, and this nonuniform decay is optimal.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605300701318658