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We demonstrate that the solutions to the Cauchy problem for the threedimensional incompressible magneto-hydrodynamics (MHD) system can developdiferent types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$.Particularly the magnetic field can develop norm inflation in short time evenwhen the velocity remains small and vice verse. Efforts are made to present avery expository development of the inginious construction of Bourgain andPavlovi\'{c} for Navier-Stokes equations.

Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$