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Ciao a tutti.
Sto scrivendo la mia tesi ed ho bisogno di aiuto. Ho diversi sitestemi di equazioni molto grandi da scrivere.
Purtroppo in alcuni casi, prima e dopo il sistema c’è uno spazio indesiderato e il numero dell’equazione va a finire in un’altra pagina. Come posso fare?
Qui sotto un estratto del codice.
Potete aiutarmi?
Grazie mille,
Nora
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\begin{document}
\chapter{Problem formulation}
%…
Find $\boldsymbol{u^+}\in \boldsymbol{H}^1(\Omega^+)$, $\boldsymbol{u^-}\in \boldsymbol{H}^1(\Omega^-)$, $p^+\in L^2(\Omega^+)$, $p^-\in L^2(\Omega^-)$ such that:
\begin{equation}
\left\{
\begin{aligned}
&\int_{\Omega^+} \frac{\partial \boldsymbol{u^+}}{\partial t} \cdot \boldsymbol{v^+} + \int_{\Omega^-} \frac{\partial \boldsymbol{u^-}}{\partial t} \cdot \boldsymbol{v^-} + \int_{\Omega^+} [(\boldsymbol{u^+} \cdot \nabla) \boldsymbol{u^+}] \cdot \boldsymbol{v^+} + \int_{\Omega^-} [(\boldsymbol{u^-} \cdot \nabla) \boldsymbol{u^-}] \cdot \boldsymbol{v^-} \\& + \frac{1}{Re} \int_{\Omega^+} [(\nabla\boldsymbol{u^+} + \nabla\boldsymbol{u^+}^T)] \cdot \nabla\boldsymbol{v^+} + \frac{1}{Re} \int_{\Omega^-} [(\nabla\boldsymbol{u^-} + \nabla\boldsymbol{u^-}^T)] \cdot \nabla\boldsymbol{v^-}\\
&+ \int_{\Gamma^+_{in}+\Gamma^+_s} \left[p^+\boldsymbol{\hat{n}^+_f} – \frac{1}{Re}(\nabla \boldsymbol{u^+} + \nabla \boldsymbol{u^+}^T )\cdot \boldsymbol{\hat{n}^+_f}\right]\cdot \boldsymbol{v^+}\\\nonumber
& + \int_{\Gamma^-_{in}+\Gamma^-_s} \left[p^-\boldsymbol{\hat{n}^-_f} – \frac{1}{Re}(\nabla \boldsymbol{u^-} + \nabla \boldsymbol{u^-}^T )\cdot \boldsymbol{\hat{n}^-_f}\right]\cdot \boldsymbol{v^-}\\\nonumber
&+\int_{\Gamma_{sym}} \left[p^+\boldsymbol{\hat{n}^+_f} – \frac{1}{Re}(\nabla \boldsymbol{u^+} + \nabla \boldsymbol{u^+}^T )\cdot \boldsymbol{\hat{n}^+_f}\right]\cdot (\boldsymbol{v^+} – \boldsymbol{v^-})\\&- \int_{\Omega^+} p^+ \nabla \cdot \boldsymbol{v^+} – \int_{\Omega^-} p^- \nabla \cdot \boldsymbol{v^-}= 0,\\
&-\int_{\Omega^+} q^+ \nabla \cdot \boldsymbol{u^+} -\int_{\Omega^-} q^- \nabla \cdot \boldsymbol{u^-} = 0,\\
&\boldsymbol{u^+}\Big|_{\Gamma^+_{in}} = \boldsymbol{u}^+_{in},
\quad \boldsymbol{u^+}\Big|_{\Gamma^+_{s}} = \boldsymbol{u}^+_s,\\
&\boldsymbol{u^-}\Big|_{\Gamma^-_{in}} = \boldsymbol{u}^-_{in},
\quad \boldsymbol{u^-}\Big|_{\Gamma^-_{s}} = \boldsymbol{u^-_s},\\
&\boldsymbol{u^+} – \boldsymbol{u^-} \Big|_{\Gamma_{sym}} = \boldsymbol{0};
\end{aligned}
\right.
\end{equation}
$\forall$ $\boldsymbol{v^+}\in \boldsymbol{H}^1(\Omega^+)$, $\boldsymbol{v^-}\in \boldsymbol{H}^1(\Omega^-)$, $q^+\in L^2(\Omega^+)$, $q^-\in L^2(\Omega^-)$.
%…
\end{document}
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