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

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

2011-10-11

arxiv.org/abs/1110.2472v2

Mathematics

Analysis of PDEs

This paper has been withdrawn by the author due to an non accurate writing in the title

Scientific paper

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.

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