 of $\tau^u_\varepsilon$ for initial data $u \in \mathcal{D}_{{\mathbf 0}}$.  **Theorem III**. Given $\delta > 0$ and a bounded set $\mathcal{K} \subseteq \mathcal{D}_{\mathbf{0}}$ at a positive distance from ${\partial}\mathcal{D}_{\mathbf{0}}$ we have 