How to ensure horizontal alignment when using overbrace function and split equations?

Question

Happy lockdown. I am currently trying to align three split equations together while using the overbrace function to describe the functions of each section (they are symmetrical but for co-ordinate direction). The current code I have is:

\begin{align}
\label{eqn:mom2}
\begin{split}
    &x : \overbrace{\rho \frac{Du}{Dt}}^\text{Convection} = \overbrace{\rho g_x - \frac{\delta p}{\delta x} }^\text{Pressure} + \overbrace{\mu (\frac{\delta^2 u}{\delta x^2} + \frac{\delta^2 u}{\delta y^2} + \frac{\delta^2 u}{\delta z^2}) }^\text{Diffusion} 
    \\ 
    &y : \rho \frac{Dv}{Dt} = \rho g_y - \frac{\delta p}{\delta y} + \mu (\frac{\delta^2 v}{\delta x^2} + \frac{\delta^2 v}{\delta y^2} + \frac{\delta^2 v}{\delta z^2})
    \\ 
    &z : \rho \frac{Dw}{Dt} = \rho g_z - \frac{\delta p}{\delta z} + \mu (\frac{\delta^2 w}{\delta x^2} + \frac{\delta^2 w}{\delta y^2} + \frac{\delta^2 w}{\delta z^2}) 
\end{split}
\end{align}

If you see the attached, the presence of the overbracket misaligns the first equation line with the other two.

Would appreciate any help massively, causing a big headache!!

Thank you in advance,

Josh

Answer 1

You were very close! I suggest you encase \text{Convection} in a \mathclap directive, effectively making it have zero width. Separately, I would increase the size of the parentheses in the "diffusion" block.

\documentclass{article}
\usepackage{mathtools} % for \mathclap macro; loads 'amsmath' automatically
\begin{document}
\begin{equation}
\label{eqn:mom2}
\begin{split}
x :\quad {\overbrace{\rho \frac{Du}{Dt}}^{\mathclap{\text{Convection}}}} &= 
  {\overbrace{\rho g_x - \frac{\delta p}{\delta x} }^{\text{Pressure}}} 
  + {\overbrace{\mu \Bigl(\frac{\delta^2 u}{\delta x^2} 
  + \frac{\delta^2 u}{\delta y^2} 
  + \frac{\delta^2 u}{\delta z^2}\Bigr)\phantom{x} }^{\text{Diffusion}}}
\\ 
y :\quad \rho \frac{Dv}{Dt} &= 
  \rho g_y - \frac{\delta p}{\delta y} 
  + \mu \Bigl(\frac{\delta^2 v}{\delta x^2} 
  + \frac{\delta^2 v}{\delta y^2} 
  + \frac{\delta^2 v}{\delta z^2}\Bigr)
\\ 
z :\quad \rho \frac{Dw}{Dt} &= 
  \rho g_z - \frac{\delta p}{\delta z} 
  + \mu \Bigl(\frac{\delta^2 w}{\delta x^2} 
  + \frac{\delta^2 w}{\delta y^2} 
  + \frac{\delta^2 w}{\delta z^2}\Bigr) 
\end{split}
\end{equation}
\end{document}