\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
 \begin{equation*}
      \mathbf g_i = 
      \begin{cases} \frac{m_i}{2}   \frac{ F_{\Gamma_{k(\mathbf r_i)}}}{ K_{\Gamma_{k(\mathbf r_i)}}} 
               \left(\mathbf v_i -  \mathbf v_{\Gamma_{k(\mathbf r_i)}} \right) &  \mbox{$k(\mathbf r_i)> 0$ (inside a reservoir),} \\
                  0                                     &  \mbox{otherwise, } 
      \end{cases}
  \end{equation*}
\end{document}

