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Gevrey class regularity of the magnetohydrodynamics equations

Published online by Cambridge University Press:  17 February 2009

Sangjeong Kim
Sangjeong Kim
Affiliation:
Korean Minjok Leadership Academy, 1334, Sosa, Anheung, Hoengsung, Kangwon, 225–823, Korea; e-mail: [email protected].
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Abstract

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In this article, we use the method of Foias and Temam to show that the strong solutions of the time-dependent magnetohydrodynamics equations in a periodic domain are analytic in time with values in a Gevrey class of functions. As immediate corollaries we find that the solutions are analytic in Hr-norms and that the solutions become smooth immediately after the initial time.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 3 , January 2002 , pp. 397 - 408
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Foias, C. and Temam, R., “Gevrey class regularity for the solutions of the Navier-Stokes equations”, J. Fund. Anal. 68 (1988) 359–369.Google Scholar
[2]Lions, J. and Magenes, E., Non-Homogeneous Boundary Value Problems and Applications (Springer, 1972).Google Scholar
[3]Sermange, M. and Temam, R., “Some mathematical questions related to the MHD equations”, Comm. Pure Appl. Math. 36 (1983) 635–664.CrossRefGoogle Scholar
[4]Temam, R., Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conference Series in Applied Mathematics 41 (SIAM,Philadelphia, PA, 1983).Google Scholar
[5]Temam, R.. Navier-Stokes Equations: Theory and Numerical Analysis (Elsevier Science Publishers B.V., 1985).Google Scholar
[6]Temam, R.. Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Volume 68 (Springer, 1988).CrossRefGoogle Scholar