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

Abstract

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 Pavlović for Navier-Stokes equation.

This paper has been withdrawn by the author due to an non accurate writing in the title