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Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods

Basil Nicolaenko; Alex Mahalov; Timofey Shilkin

Séminaire Équations aux dérivées partielles

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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