We consider the wave equation \left{ \begin{array}{ll} u_{tt}(x,t)-\Delta u(x,t)=0, x \in \Omega, t>0\\ u=0, \quad u \in \partial \Omega, t>0 \\ u(0,x)=u_{0}(x), \quad u_{t}(0,x)=u_{1}(x), x \in \Omega \end{array} \right. \end{equation}. the energy functional $E(t)$ is \begin{equation} E(t)=\dfrac{1}{2}\Vert u_{t}(t)\Vert_{2}^{2}+\dfrac{1}{2}\Vert \nabla u(t)\Vert_{2}^{2} \end{equation} How can I estimate $\Vert \Delta u(t)\Vert_{2}$ in term of $E(t)$ or can we find a constant $c>0$ such that $\Vert \Delta u(t)\Vert_{2}^{2}\leq cE(t) $?