\displaystyle E(T) \leq \int_{{\bf R}^d} |u_0|^2\ dx - \nu \int_0^T \int_{{\bf R}^d} |\nabla u|^2 + |\nabla v|^2\ dx dt - \int_{{\bf R}^d} u(T) \cdot v(T)\ dx \ \ \ \ \ (27)