We introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $\dot B^{-1+\frac{3}{p}}_{p,\infty}$, $p > 3$. Our solutions satisfy certain stability properties with respect to the weak-$\ast$ convergence of initial data. We provide applications to blow-up criteria, minimal blow-up initial data, and forward self-similar solutions. 查看全文>>