Problem in showing partial derivatives in a table

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I'm writing the manuscript of my paper and I have to write partial derivatives in a table. While doing so, there is a problem when I use \begin{equation}...\end{equation} in table. For simplicity, I write a part of table as follows:

\begin{tabular}{ccc}
\toprule
  Boundary &  Flow  \\
\midrule
  Inlet &   
  \[ \textit {u=U_0, v=0}\]\\
  Outlet & 
  \[  {\frac{\partial u}{\partial y}=\frac{\partial v}{\partial x}=0}\]\\

\bottomrule
\end{tabular}

I would be grateful if someone give me a help with this issue.
I have to mention that when I use the same equation NOT in table, the code is applied well:

\begin{equation}
 {\frac{\partial u}{\partial y}=\frac{\partial v}{\partial x}=0}
\end{equation}

Answer 1

Here is a solution, without equation numbers, with the esdiff package:

    \documentclass{article}
    \usepackage{amsmath}
    \usepackage{esdiff}
    \usepackage{array, booktabs}

    \begin{document}

    \begin{tabular}{c >{$}wc{3cm}<{$}}
    \toprule
      Boundary & \text{Flow} \\
    \midrule
      Inlet &
      u=U_0, v=0 \\[1ex]
      Outlet &
     \diffp{u}{y} =\diffp{v}{x} =0 \\
    \bottomrule
    \end{tabular}

    \end{document}