Abstract:

The magnetohydrodynamics (MHD) equations describe the interaction between the velocity field and the magnetic field governed by the coupling between the Navier—Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetism. In this talk, we will introduce a construction of both self-similar (SS) and discretely self-similar (DSS) local Leray solutions to MHD equations with large weak L^3 initial data. The approach of this work is based on a work by Bradshaw and Tsai for Navier—Stokes equations, and is under the supervision of Prof. Tsai at University of British Columbia.