Ill-posedness of the stationary Navier-Stokes equations in Besov spaces

Abstract

The solutions of the stationary Navier-Stokes equations in Rn for n≥3 in the scaling invariant Besov spaces are investigated. It is proved that a sequence of bounded smooth external forces whose B˙∞,1−3 norms converges to zero can produce a sequence of bounded smooth solutions whose B˙−1∞,∞ norms never converges to zero. Such norm inflation phenomena are shown by constructing the sequence of external forces, as similar to those of initial data proposed by Bourgain-Pavlović in the non-stationary problem.