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

@article{Dai2011NormIF, title={Norm inflation for incompressible magneto-hydrodynamic system in \$\dot\{B\}\_\{\infty\}^\{-1,\infty\}\$}, author={Mimi Dai and Jie Qing and Maria E. Schonbek}, journal={Advances in Differential Equations}, year={2011} }

Author(s): Dai, Mimi; Qing, Jie; Schonbek, Maria | 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…

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