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Find $X_i\in V$ et $Y_i\in V$, $i=\{1, \ldots, 5\}$, such that $$\begin{eqnarray*} \int_\Omega (Y'_i+\tau_{\rm e}\, \vec{v}\cdot\nabla Y'_i)\, (\vec{v}\cdot\nabla X_i-Y_i) \;{\rm d}\Omega = 0\;, && \forall Y'_i \in V \;, \\ \int_\Omega (X'_i+\tau_{\rm e}\, \vec{v}\cdot\nabla X'_i)\, (\vec{v}\cdot\nabla Y_i-f_i) \;{\rm d}\Omega = 0\;, && \forall X'_i \in V \;, \end{eqnarray*}$$ with $$\begin{equation*} V = \{ f(x,y)\in H^1(\Omega):\, f(0,0)=0\} \;. \end{equation*}$$