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\begin{document}

\section{File 1Introduction}
\label{sec:introduction}

(\ref{eq:main:1})
This is the external file

New test
\begin{equation}
\label{eq:file1:1}
\int f dx
\end{equation}

\begin{subequations}
\label{E:EULERPOISSON}
\begin{alignat}{2}
\partial_t\rho + \text{div}\, (\rho \mathbf{u})& = 0 &&\ \text{ in } \ B(t)\,;\label{E:CONTINUITYEP}\\
\rho\left(\partial_t  \mathbf{u}+ ( \mathbf{u}\cdot\nabla) \mathbf{u}\right) +\nabla p &=-\rho \nabla\Phi&&\ \text{ in } \ B(t)\,;\label{E:VELOCITYEP}\\
\Delta \Phi  = 4\pi c\,\rho, \ \lim_{|x|\to\infty}\Phi(t,x) & = 0&& \ \text{ in } \ {\mathbb R}^3 \,; \label{E:POISSON}\\
%\lim_{|x|\to\infty}\Phi(t,x) & = 0; && \label{E:POISSONBOUNDARY}\\
p&=0&& \ \text{ on } \ \partial B(t) \,;\label{E:VACUUMEP} \\
\mathcal{V}_{\partial B(t)}&= \mathbf{u}\cdot \mathbf{n}(t)  && \ \text{ on } \ \partial B(t)\,;\label{E:VELOCITYBDRYEP}\\
(\rho(0,\cdot),  \mathbf{u}(0,\cdot))=(\rho_0,  \mathbf{u}_0)\,, & \ B(0)=B_0&&\,.\label{E:INITIALEP}
\end{alignat}
\end{subequations}


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