Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
Basil Nicolaenko, Alex Mahalov, Timofey Shilkin (2006-2007)
Séminaire Équations aux dérivées partielles
Similarity:
We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.