Norm inflation for incompressible magneto-hydrodynamic system ]{Norm   inflation for incompressible magneto-hydrodynamic system in   $\dot{B}_{\infty}^{-1,\infty}$
  We demonstrate that the solutions to the Cauchy problem for the three dimensional incompressible magneto-hydrodynamics (MHD) system can develop diferent types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$. Particularly the magnetic field can develop norm inflation in short time even when the velocity remains small and vice verse. Efforts are made to present a very expository development of the inginious construction of Bourgain and Pavlovi\'{c} for Navier-Stokes equation. 
Mimi Dai, Jie Qing, and Maria Schonbek
math.AP