Norm inflation for generalized magneto-hydrodynamic system

@article{Cheskidov2014NormIF,
  title={Norm inflation for generalized magneto-hydrodynamic system},
  author={Alexey Cheskidov and Mimi Dai},
  journal={Nonlinearity},
  year={2014},
  volume={28},
  pages={129 - 142}
}
We consider the incompressible magneto-hydrodynamic system with fractional powers of the Laplacian in the three-dimensional case. We discover a wide range of spaces where the norm inflation occurs and hence small initial data results are out of reach. The norm inflation occurs not only in scaling invariant (critical) spaces, but also in supercritical and, surprisingly, subcritical ones. 

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