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


We prove that if an initial datum to the incompressible Navier-Stokes equations in any critical Besov space Ḃ −1+ 3 p p,q (R ), with 3 < p, q < ∞, gives rise to a strong solution with a singularity at a finite time T > 0, then the norm of the solution in that Besov space becomes unbounded at time T . This result, which treats all critical Besov spaces where… (More)