In this paper, we mainly prove the existence of the minimal blow-up initial data in critical Fourier-Herz space $F\dot{ B}^{ 2-{ \frac3p}}_{ p,q}(\RR^3)$ with $1<p\leq\infty$ and $1\leq q<\infty$ for the three dimensional incompressible potential Navier-Stokes equations by developing techniques of "localization in space" involving the partial regularity given by the De Giorgi iteration, weak-strong uniqueness, the short-time behaviour of the kinetic energy and stability of singularity of Calder\'on's solution.
Categories: math.AP