Como formatar um longo sistema de equações

Question

Eu queria saber como é possível formatar longos sistemas de equações onde as equações precisam ser quebradas. Eu quero replicar isso

Aqui estão as 3 equações digitadas:

    \begin{equation}
    \frac{\partial u_r}{\partial t}+u_r\frac{\partial u_r}{\partial r}+\frac{u_{\theta }}{r}\frac{\partial u_r}{\partial \theta }-\frac{u_{\theta }^2}{r}+u_z\frac{\partial u_r}{\partial z}=\frac{\mu }{\rho \:}\left[\frac{\partial }{\partial r}\left(\frac{1}{r}\frac{\partial }{\partial r}\left(ru_r\right)\right)+\frac{1}{r^2}\frac{\partial ^2u_r}{\partial \theta ^2}+\frac{\partial ^2u_r}{\partial z^2}-\frac{2}{r^2}\frac{\partial u_{\theta }}{\partial \theta }\right]-\frac{1}{\rho }\frac{\partial P}{\partial r}
\end{equation}

\begin{equation}
    \frac{\partial u_{\theta }}{\partial t}+u_r\frac{\partial u_{\theta }}{\partial r}+\frac{u_{\theta }}{r}\frac{\partial u_{\theta }}{\partial \theta }-\frac{u_ru_{\theta }}{r}+u_z\frac{\partial u_{\theta }}{\partial z}=\frac{\mu }{\rho \:}\left[\frac{\partial }{\partial r}\left(\frac{1}{r}\frac{\partial }{\partial r}\left(ru_{\theta }\right)\right)+\frac{1}{r^2}\frac{\partial ^2u_{\theta }}{\partial \theta ^2}+\frac{\partial ^2u_{\theta }}{\partial z^2}+\frac{2}{r^2}\frac{\partial u_{\theta }}{\partial \theta }\right]-\frac{1}{r\rho }\frac{\partial P}{\partial \theta }
\end{equation}

\begin{equation}
    \frac{\partial u_z}{\partial t}+u_r\frac{\partial u_z}{\partial r}+\frac{u_{\theta }}{r}\frac{\partial u_z}{\partial \theta }+u_z\frac{\partial u_z}{\partial z}=\frac{\mu }{\rho \:}\left[\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial u_z}{\partial \:r}\right)+\frac{1}{r^2}\frac{\partial ^2u_z}{\partial \theta ^2}+\frac{\partial ^2u_z}{\partial z^2}\right]-\frac{1}{\rho }\frac{\partial P}{\partial \theta }+g_z
\end{equation}

Posso dividir as equações individualmente, mas não sei como listá-las no formato mostrado acima. Qualquer coisa ajuda. Obrigado.

Answer 1

Algo assim:

Eu usei um align*ambiente doamsmathpacote com alinhamento após o primeiro sinal + e alguns \notagcomandos para suprimir números de equações intermediárias. Ao contrário do OP, sugiro fortemente que os iguais comecem na segunda linha das equações, em vez de estarem no final da primeira linha.

Aqui está o código:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

   \begin{align}
      \frac{\partial u_r}{\partial t}+&u_r\frac{\partial u_r}{\partial r}
        +\frac{u_{\theta }}{r}\frac{\partial u_r}{\partial \theta }
        -\frac{u_{\theta }^2}{r}+u_z\frac{\partial u_r}{\partial z}
      \\ &=\frac{\mu }{\rho \:}\left[\frac{\partial }{\partial r}
          \left(\frac{1}{r}\frac{\partial }{\partial r}\left(ru_r\right)\right)
            +\frac{1}{r^2}\frac{\partial ^2u_r}{\partial \theta ^2}
            +\frac{\partial ^2u_r}{\partial z^2}
            -\frac{2}{r^2}\frac{\partial u_{\theta }}{\partial \theta }\right]
            -\frac{1}{\rho }\frac{\partial P}{\partial r}\notag\\
      \frac{\partial u_{\theta }}{\partial t}+&u_r\frac{\partial u_{\theta }}{\partial r}
           +\frac{u_{\theta }}{r}\frac{\partial u_{\theta }}{\partial \theta }
                -\frac{u_ru_{\theta }}{r}+u_z\frac{\partial u_{\theta }}{\partial z}\\
        &=\frac{\mu }{\rho \:}\left[\frac{\partial }{\partial r}
              \left(\frac{1}{r}\frac{\partial }{\partial r}\left(ru_{\theta }\right)\right)
              +\frac{1}{r^2}\frac{\partial ^2u_{\theta }}{\partial \theta ^2}
              +\frac{\partial ^2u_{\theta }}{\partial z^2}
              +\frac{2}{r^2}\frac{\partial u_{\theta }}{\partial \theta }\right]
              -\frac{1}{r\rho }\frac{\partial P}{\partial \theta }
      \notag\\
      \frac{\partial u_z}{\partial t}+&u_r\frac{\partial u_z}{\partial r}
          +\frac{u_{\theta }}{r}\frac{\partial u_z}{\partial \theta }
              +u_z\frac{\partial u_z}{\partial z}\\
          &=\frac{\mu }{\rho \:}\left[\frac{1}{r}\frac{\partial }{\partial r}
              \left(r\frac{\partial u_z}{\partial \:r}\right)
                  +\frac{1}{r^2}\frac{\partial ^2u_z}{\partial \theta ^2}
                      +\frac{\partial ^2u_z}{\partial z^2}\right]
                          -\frac{1}{\rho }\frac{\partial P}{\partial \theta }+g_z\notag
  \end{align}

\end{document}

Answer 2

Outro código com alinhamento, mas incluindo as descrições à esquerda, e uma sintaxe mais simples com o diffcoeffpacote:

\documentclass{article}
\usepackage{geometry} 
\usepackage{amsmath}
\usepackage{diffcoeff} 

\begin{document}

\begin{align}
r\text{-momentum:} & & & \diffp{u_r}{t} + u_r\diffp{u_r}{r} + \frac{u_{\theta }}{r}\diffp{u_r}{\theta }-\frac{u_{\theta }^2}{r} + u_z\diffp{u_r}{z} = \\
\notag & & & \frac{\mu }{\rho \:}\left[\diffp{}{r}\left(\frac{1}{r}\diffp{}{r}\left(ru_r\right)\right) + \frac{1}{r^2}\diffp[2]{u_r}{\theta} + \diffp[2]{u_r}{z}-\frac{2}{r^2}\diffp{u_{\theta }}{\theta }\right]-\frac{1}{\rho }\diffp{P}{r}\\[2ex]
%
\theta\text{-momentum:} & & & \diffp{u_{\theta }}{t} + u_r\diffp{u_{\theta }}{r} + \frac{u_{\theta }}{r}\diffp{u_{\theta }}{\theta }-\frac{u_ru_{\theta }}{r} + u_z\diffp{u_{\theta }}{z} = \\
\notag & & & \frac{\mu }{\rho \:}\left[\diffp{}{r}\left(\frac{1}{r}\diffp{}{r}\left(ru_{\theta }\right)\right) + \frac{1}{r^2}\diffp[2]{u_{\theta }}{\theta} + \diffp[2]{u_{\theta }}{z} + \frac{2}{r^2}\diffp{u_{\theta }}{\theta }\right]-\frac{1}{r\rho }\diffp{P}{\theta } \\[2ex]
%
z\text{-momentum:} & & & \diffp{u_z}{t} + u_r\diffp{u_z}{r} + \frac{u_{\theta }}{r}\diffp{u_z}{\theta } + u_z\diffp{u_z}{z} = \\
 \notag & & & \frac{\mu }{\rho \:}\left[\frac{1}{r}\diffp{}{r}\left(r\diffp{u_z}{\:r}\right) + \frac{1}{r^2}\diffp[2]{u_z}{\theta} + \diffp[2]{u_z}{z}\right]-\frac{1}{\rho }\diffp{P}{\theta } + g_z
\end{align}

\end{document}