  In this paper, we consider the inviscid limit problem to the higher
dimensional incompressible Navier--Stokes equations in the whole space. It is
shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data
$u_0\in B^{s}_{p,r}$ and for some $T>0$, the solutions of the Navier--Stokes
equations converge strongly in $L^\infty_TB^{s}_{p,r}$ to the Euler equations
as the viscosity parameter tends to zero. We furthermore prove the failure of
the uniform (with respect to the initial data) $B^{s}_{p,r}$ convergence in the
inviscid limit of a family of solutions of the Navier-Stokes equations towards
a solution of the Euler equations.
