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Basil Nicolaenko; Alex Mahalov; Timofey Shilkin
Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
Séminaire Équations aux dérivées partielles (Polytechnique) (2006-2007), Exp. No. 21, 19 p.
Article PDF | Reviews MR 2385208

Résumé - Abstract

We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space $L^3 (\mathbf{R}^3)$. This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally $L^3$. We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.


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