1

desired form

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.

enter image description here

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

3

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} 

enter image description here

  • Actually, my society denote Laplacian by \triangle. Thanks! This is really nice. – Will Kwon Dec 28 '17 at 11:40
1

You can use aligned inside cases, but I'd prefer not to align at the equals signs.

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator{\Div}{div}

\begin{document}

With alignment at the equals sign:
\[
\begin{cases}
\begin{aligned}
-\triangle u +u \cdot \nabla u +\nabla p &= f && \text{in $\Omega$}, \\
\Div u                                   &= 0 && \text{in $\Omega$}, \\
u                                        &= 0 && \text{on $\partial \Omega$},
\end{aligned}
\end{cases}
\]

Without alignment:
\[
\begin{dcases*}
-\triangle u +u \cdot \nabla u +\nabla p = f & in $\Omega$, \\
\Div u = 0                                   & in $\Omega$, \\
u = 0                                        & on $\partial \Omega$,
\end{dcases*}
\]

\end{document}

enter image description here

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