Blow-up of critical Besov norms at a potential Navier-Stokes singularity

Isabelle Gallagher, Gabriel S. Koch, Fabrice Planchon

We prove that if an initial datum to the incompressible Navier-Stokes equations in any critical Besov space ${\dot{B}}_{p,q}^{-1+\frac{3}{p}}({\mathbb{R}}^3)$, with $3<p,q<\infty$, gives…