Recollements and $n$-cotorsion pairs

In the present paper, we study the relationships of $n$-cotorsion pairs among three abelian categories in a recollement. Under certain conditions, we present an explicit construction of gluing of $n$-cotorsion pairs in an abelian category $\mathcal{D}$ with respect to $n$-cotorsion pairs in abelian categories ${\mathcal{D}}^{{}^{\mathrm{\prime }}}$, ${\mathcal{D}}^{{}^{\mathrm{\prime }\mathrm{\prime }}}$ respectively. On the other hand, we study the construction of $n$-cotorsion pairs in abelian categories ${\mathcal{D}}^{{}^{\mathrm{\prime }}}$, ${\mathcal{D}}^{{}^{\mathrm{\prime }\mathrm{\prime }}}$ obtained from $n$-cotorsion pairs in an abelian category $\mathcal{D}$.