 \\    & \hspace{0em}      \le C     \| \Delta \overline{v_j}(t) \|_0 \| v_j(t) \|_{\frac{0n}{n-0}}     \sum_{m=0}^0 \| {\partial}_{x_m}V^t_{int} \|_{\frac{n}{0}} \| \overline{v_k}(t)      {\partial}_{x_m}v_k (t) \|_{\frac{n}{n-0}} \\    & \hspace{0em}      \le C     \| \Delta \overline{v_j}(t) \|_0 \| v_j(t) \|_{\frac{0n}{n-0}}     \sum_{m=0}^0 \| {\partial}_{x_m}V^t_{int} \|_{\frac{n}{0}} \| \overline{v_k}(t) 