Well‐posedness for fractional Navier–Stokes equations in the largest critical spaces Ḃ ∞ , ∞ − ( 2 β − 1 ) ( R n )

This note studies the well‐posedness of the fractional Navier–Stokes equations in some supercritical Besov spaces as well as in the largest critical spacesḂ ∞ , ∞ − ( 2 β − 1 )(R n) for β  ∈ (1/2,1). Meanwhile, the well‐posedness for fractional magnetohydrodynamics equations in these Besov spaces is also studied. Copyright © 2012 John Wiley & Sons, Ltd.