Equations (to be tagged, but how?) too long to fit in a Beamer alertblock

Question

In the following code the 3rd equation is going out of the alert block. I want to align those equations beautifully inside the alert block. And also I want to indicate that the first equation is 'Mass conservation', second is 'Momentum conservation' and last as 'Total fluid energy conservation'. How can I do that?

\documentclass[handout,13pt,compress,c]{beamer}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{mathtools}
\usetheme{PaloAlto}

\begin{document}

\begin{frame}
\frametitle{Physical equations}
\framesubtitle{The equations that we are solving by Enzo during the simulation}

\begin{alertblock}{Eulerian equations of ideal magnetohydrodynamics (MHD) including    gravity, in comoving coordinate}
$$ \dfrac{\partial \rho }{\partial t} + \dfrac{1}{a}\nabla .(\rho \vec{v}) = 0 $$
$$ \dfrac{\partial \rho \vec{v}}{\partial t} + \dfrac{1}{a}\nabla .\left(\rho \vec{v}\vec{v} + \vec{I}p^* - \dfrac{\vec{B}\vec{B}}{a}\right) = -\dfrac{\dot{a}}{a}\rho \vec{v} - \dfrac{1}{a}\rho \nabla \phi $$
$$ \dfrac {\partial E} {\partial t} + \dfrac {1}{a} \nabla . \left[ (E+p^*) - \dfrac{1}{a}\vec{B}(\vec{B}.\vec{v})\right] = - \dfrac{\dot{a}}{a}\left( 2E - \dfrac{B^2}{2a}\right) - \dfrac{\rho }{a}\vec{v}.\nabla \phi - \Lambda + \Gamma + \dfrac{1}{a^2}\nabla . \vec{F}_{cond}, $$

\end{alertblock}
\end{frame}

\end{document}

Answer 1

Here is one option using alignat*

\documentclass[handout,13pt,compress,c]{beamer}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{mathtools}
\usetheme{PaloAlto}

\begin{document}

\begin{frame}
  \frametitle{Physical equations}
  \framesubtitle{The equations that we are solving by Enzo during the
simulation}

  \begin{alertblock}{Eulerian equations of ideal magnetohydrodynamics (MHD)
including    gravity, in comoving coordinate}
\[ \frac{\partial \rho }{\partial t} + \frac{1}{a}\nabla .(\rho \vec{v}) =
    0
\]
\[ \frac{\partial \rho \vec{v}}{\partial t} + \dfrac{1}{a}\nabla
    .\left(\rho \vec{v}\vec{v} + \vec{I}p^* - \frac{\vec{B}\vec{B}}{a}\right) =
    -\frac{\dot{a}}{a}\rho \vec{v} - \frac{1}{a}\rho \nabla \phi 
\]
    \begin{alignat*}{2}
      \frac {\partial E} {\partial t} + \frac {1}{a} \nabla . \left[ (E+p^*) -
        \frac{1}{a}\vec{B}(\vec{B}.\vec{v})\right] &= &&-
      \frac{\dot{a}}{a}\left(2E - \frac{B^2}{2a}\right) \\
      & &&  - \frac{\rho}{a}\vec{v}.\nabla \phi
      - \Lambda + \Gamma\\
      & && + \dfrac{1}{a^2}\nabla . \vec{F}_{cond},
    \end{alignat*}

  \end{alertblock}
\end{frame}

\end{document}

---

Also, you don't need \dfrac in display math and you should use \[\] over double dollars.

Why is \[ ... \] preferable to $$ ... $$?

---

By naming, do mean numbering and referencing a label name later on?

\begin{align}                                                                   
      \dfrac{\partial \rho }{\partial t} + \dfrac{1}{a}\nabla .(\rho \vec{v}) &=    
    0\label{eqname}\\                                                               
    \dfrac{\partial \rho \vec{v}}{\partial t} + \dfrac{1}{a}\nabla                  
    .\left(\rho \vec{v}\vec{v} + \vec{I}p^* - \dfrac{\vec{B}\vec{B}}{a}\right)      
    &=                                                                              
    -\dfrac{\dot{a}}{a}\rho \vec{v} - \dfrac{1}{a}\rho \nabla                       
\phi\label{eq2name}                                                                 
    \end{align}
     \vspace*{-.6cm}        \begin{alignat}{2}                                                              
      \dfrac {\partial E} {\partial t} + \dfrac {1}{a} \nabla . \left[ (E+p^*) -   
        \dfrac{1}{a}\vec{B}(\vec{B}.\vec{v})\right] &= &&-                          
      \dfrac{\dot{a}}{a}\left(2E - \dfrac{B^2}{2a}\right) \notag\\                  
      & &&  - \frac{\rho}{a}\vec{v}.\nabla \phi                                     
      - \Lambda + \Gamma\notag\\                                                    
      & && + \dfrac{1}{a^2}\nabla . \vec{F}_{cond},\label{eq3name}                  
    \end{alignat}

---

To change the numbers to names, add \tag{name}.

\begin{align}                                                                       
  \dfrac{\partial \rho }{\partial t} + \dfrac{1}{a}\nabla .(\rho \vec{v}) &=        
  0\tag{Mass Conservation}\\                                          
  \dfrac{\partial \rho \vec{v}}{\partial t} + \dfrac{1}{a}\nabla                    
  .\left(\rho \vec{v}\vec{v} + \vec{I}p^* - \dfrac{\vec{B}\vec{B}}{a}\right)        
  &=                                                                                
  -\dfrac{\dot{a}}{a}\rho \vec{v} - \dfrac{1}{a}\rho \nabla                         
  \phi\tag{Momentum Conservation}                                   
\end{align}
\vspace*{-.6cm}
\begin{alignat}{2}                                                                  
  \dfrac {\partial E} {\partial t} + \dfrac {1}{a} \nabla . \left[ (E+p^*) -        
    \dfrac{1}{a}\vec{B}(\vec{B}.\vec{v})\right] &= &&-                              
  \dfrac{\dot{a}}{a}\left(2E - \dfrac{B^2}{2a}\right) \notag\\                      
  & &&  - \frac{\rho}{a}\vec{v}.\nabla \phi                                         
  - \Lambda + \Gamma\notag\\                                                        
  & && + \dfrac{1}{a^2}\nabla . \vec{F}_{cond},                                     
  \tag{Total Fluid Energy}                                           
\end{alignat}

Answer 2

What "beautifully aligned" means here is open to interpretation. Since tags are reguired and space is limited, I would

• locally set the font size to \footnotesize
• opt for a gather environment combined with two split environments.

In order to avoid confusion, it's also probably a good idea to leave more vertical space between successive equations than a simple line break would.

\documentclass[handout,13pt,compress,c]{beamer}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{mathtools}
\usetheme{PaloAlto}

\begin{document}

\begin{frame}
\frametitle{Physical equations}
\framesubtitle{The equations that we are solving by Enzo during the simulation}

\begin{alertblock}{Eulerian equations of ideal magnetohydrodynamics (MHD)
    including gravity, in comoving coordinate}
\footnotesize
\begin{gather*}
    \dfrac{\partial \rho }{\partial t} + \dfrac{1}{a}\nabla .(\rho \vec{v}) =
        0 \tag{Mass Conservation} \\[1em]
    \begin{split}
    &\dfrac{\partial \rho \vec{v}}{\partial t} + \dfrac{1}{a}\nabla .
        \left(\rho \vec{v}\vec{v} + \vec{I}p^* - \dfrac{\vec{B}\vec{B}}{a}\right) \\
    &\qquad = -\dfrac{\dot{a}}{a}\rho \vec{v} - \dfrac{1}{a}\rho \nabla \phi 
    \end{split} \tag{Momentum Conservation}\\[1em]
    \begin{split}
        &\dfrac {\partial E} {\partial t} + \dfrac {1}{a} \nabla . \left[ (E+p^*)
            - \dfrac{1}{a}\vec{B}(\vec{B}.\vec{v})\right] \\
        &\qquad = - \dfrac{\dot{a}}{a}\left( 2E - \dfrac{B^2}{2a}\right) -
            \dfrac{\rho }{a}\vec{v}.\nabla \phi - \Lambda\\
        &\qquad \phantom{=} + \Gamma + \dfrac{1}{a^2}\nabla . \vec{F}_{cond}, 
    \end{split} \tag{Total Fluid Energy}
\end{gather*}
\end{alertblock}
\end{frame}

\end{document}