[Tex/LaTex] mathtools: cases inside alignment

Question

Hi. I have struggled with aligning with cases environment The minimal example of the above thing is the following:

\documentclass{article}
\usepackage{mathtools}

\makeatletter
\newcases{PDEcases}{\quad}{%
  \hfil$\m@th\displaystyle{##}$}{{##}\hfil}{\lbrace}{.}
\makeatother

\begin{document}
\[
\begin{PDEcases} 
-\triangle u +u \cdot \nabla u +\nabla p =f&in  $\Omega$\\
\mathrm{div}\, u =0& in  $\Omega$\\
u=0& on  $\partial \Omega$,
\end{PDEcases}
\]

Alignment inside cases

\[
\begin{dcases*} 
-\triangle u +\nabla p =-w\cdot \nabla w +f&in  $\Omega$\\
\hspace{2.75em}\mathrm{div}\, u =0& in  $\Omega$\\
\hspace{4.2em}u=0& on  $\partial \Omega$,
\end{dcases*}
\]
\end{document}

For the first case, using \newcases, I can easily make a custom environment on cases. But I want to make an equation like second form. But I failed to make an equation with cases environment. I manually adjust it by using \hspace.

How can I make it more smarter way?

One possible solution of mine is to use the alignedat enviornment. But it is not a case environment.

Here is a code:

\[
 \left\{
\begin{alignedat}{2} 
-\triangle u +\nabla p &=-w\cdot \nabla w +f&&\qquad \mbox{in  $\Omega$},\\
\mathrm{div}\, u &=0&&\qquad  \mbox{in  $\Omega$},\\
u&=0 &&\qquad \mbox{on  $\partial \Omega$},
\end{alignedat} \right.
\]

I'm unsatisfied with \quad part and \left\{ \right. Is there anyway to make it using cases stuff?

Thanks in advances

Answer 1

Here is a solution with cases. I've added another solution, which has a better vertical spacing, in my opinion, and a shorter code, with the empheq package (which loads mathtools).

Also I replaced \triangle with the more correct Delta, and defined div as a Math Operator:

\documentclass{article}
\usepackage{empheq}

\DeclareMathOperator{\Div}{div}
\begin{document}

\[
\begin{dcases}
\begin{aligned}
-\Delta u +\nabla p & =-w\cdot \nabla w +f \\
\Div u & =0 \\
u & =0
\end{aligned}
 &
\begin{aligned}
 & \text{in } \Omega, \\
& \text{in } \Omega, \\
& \text{on }\partial \Omega.
\end{aligned}
\end{dcases}
\]
\bigskip

\begin{empheq}[left = \empheqlbrace]{alignat* = 2}
    -\Delta u +\nabla p & =-w\cdot \nabla w +f &\quad & \text{in } \Omega, \\
    \Div u & = 0&\quad & \text{in } \Omega, \\
u & =0 & & \text{on }\partial \Omega.
\end{empheq}

\end{document}