\documentclass{article}

\begin{document}
\begin{equation}
  U \frac{\partial c}{\partial x}+V\frac{\partial c}{\partial y} -
  \nabla \cdot ( k \nabla c) + a c = f
\end{equation}

\begin{equation}
  k = \left[ 
  \begin{array}{c c}
    k11 & k12 \\
    k12 & k22
  \end{array}
\right]
\end{equation}
\begin{equation}
\frac{\partial u}{\partial t}+  u \frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y} =
  - \frac{\partial p}{\partial x} + \frac{1}{Re} \nabla^2 u 
\end{equation}
\begin{equation}
\frac{\partial v}{\partial t}+  u \frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y} =
  - \frac{\partial p}{\partial y} + \frac{1}{Re} \nabla^2 v 
\end{equation}
\begin{equation}
  \nabla \cdot \vec{u} = 0
\end{equation}
\end{document}
