A lateral brace to group a set of equations with labels

Use empheq.

\documentclass{article}
\usepackage{amsmath,empheq}
\begin{document}
\begin{empheq}[left=\empheqlbrace]{align}
&\nabla\times\bar E = -\frac{\partial\bar B}{\partial t}-\bar J_{\text{mi}} \\
&\nabla\times\bar H = \bar J + \bar J_i + \frac{\partial\bar D}{\partial t}\\
&\nabla\cdot\bar J + \nabla\cdot\bar J_i = - \frac{\partial\rho}{\partial t}\\
&\nabla\cdot\bar J_{\text{mi}} = - \frac{\partial\rho_{\text{mi}}}{\partial t}\\
&\nabla\cdot\bar D = \rho\\
&\nabla\cdot\bar B = \rho_m
\end{empheq}
\end{document} 

Perhaps you should try this:

\newcommand{\pd}[2]{\frac{\partial{#1}}{\partial{#2}}}

\begin{eqnarray}
  \left\{
  \begin{aligned}
    \del\times\vec{E}&\;=\;-\pd{\vec{B}}{t}-...\\
    \del\times\vec{E}&\;=\;\vec{J}+...\\
    .
    .
    .
  \end{aligned}
  \right.
\end{eqnarray}