Ill-posedness of basic equations of fluid dynamics in Besov spaces

A. Cheskidov, R. Shvydkoy

We give a construction of a divergence-free vector field $u_0\in H^s\cap B_{\infty ,\infty }^{-1}$, for all $s<1/2$, such that any Leray-Hopf solution to the Navier-Stokes equation…