2 problems

Existence conjecture. Even strictly positive densities $w$ exist that do not satisfy condition and for which the uniqueness asserted in Theorem fails.

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…