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) $?