Publication Cover
Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 7
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Original Articles

Wellposedness for the magnetohydrodynamics equation in critical space

Pages 773-785 | Received 14 Sep 2007, Accepted 12 Jun 2008, Published online: 29 Sep 2008
 

Abstract

In this article, we study wellposedness of magnetohydrodynamics equation in Besov space in ℝ3 × [0, T]. Comparing to Kato's space [T. Kato, Strong L p solutions of the Navier–Stokes equations in m with applications to weak solutions, Math. Z 187 (1984), pp. 471–480] for Navier–Stokes equation, we give existence and uniqueness of the solution of MHD in with (p, q, r) ∈ [1, ∞] × [2, ∞] × [1, ∞] such that by applying contraction argument directly. Moreover, we find that the bilinear operator ℬ seeing below is continuous from to for which improves the well-known result for r = ∞.

AMS Subject Classifications: :

Acknowledgement

The author would like to thank Professor Y. Chemin for sending his lecture.

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