Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 21, 19 p.

We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space L 3 (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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Nicolaenko, Basil; Mahalov, Alex; Shilkin, Timofey. Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 21, 19 p. http://archive.numdam.org/item/SEDP_2006-2007____A21_0/

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