2 problems

Let $u\in C\left(\left[0,T_{max}\right);\dot{H}^1_{df}\right)$ be a smooth solution of the Navier–Stokes equation with finite maximal existence time $T_{max}<+\infty$. Let…

Consider the weighted space $L^{p}_{|x|^{\frac{\alpha p}{}}d|x|}L^{\widetilde{p}}_{\theta}$ for Navier–Stokes initial data, with scaling-critical relation $\alpha=1-\frac{n}{p}$. I…