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In this paper, we consider the inviscid limit problem to the higherdimensional incompressible Navier--Stokes equations in the whole space. It isshown 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--Stokesequations converge strongly in $L^\infty_TB^{s}_{p,r}$ to the Euler equationsas the viscosity parameter tends to zero. We furthermore prove the failure ofthe uniform (with respect to the initial data) $B^{s}_{p,r}$ convergence in theinviscid limit of a family of solutions of the Navier-Stokes equations towardsa solution of the Euler equations.

Loss of Uniform Convergence for Solutions of the Navier--Stokes Equations in the Inviscid Limit