We consider the three-dimensional incompressible magneto-hydrodynamic system
with fractional powers of the Laplacian. 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.Comment: 14 page

Cheskidov, Alexey