Recollements associated to cotorsion pairs over upper triangular matrix rings

Let $A$, $B$ be two rings and $T=\left(\begin{smallmatrix} A & M 0 & B \end{smallmatrix}\right)$with$M$an$A$-$B$-bimodule. Given two complete hereditary cotorsion pairs $({\mathcal{A}}_A,{\mathcal{B}}_A)$ and $({\mathcal{C}}_B,{\mathcal{D}}_B)$ in $A$-Mod and $B$-Mod respectively. We define two cotorsion pairs $(\Phi($\mathcal{A}${A},$\mathcal{C}${B}), $\mathrm{R}\mathrm{e}\mathrm{p}$($\mathcal{B}${A},$\mathcal{D}${B}))$and$($\mathrm{R}\mathrm{e}\mathrm{p}$($\mathcal{A}${A},$\mathcal{C}${B}), \Psi($\mathcal{B}${A},$\mathcal{D}${B}))$in$T$-Mod and show that both of these cotorsion pairs are complete and hereditary. Given two cofibrantly generated model structures ${\mathcal{M}}_A$ and ${\mathcal{M}}_B$ on $A$-Mod and $B$-Mod respectively. Using the result above, we investigate when there exist a cofibrantly generated model structure ${\mathcal{M}}_T$ on $T$-Mod and a recollement of $\mathrm{H}\mathrm{o}({\mathcal{M}}_T)$ relative to $\mathrm{H}\mathrm{o}({\mathcal{M}}_A)$ and $\mathrm{H}\mathrm{o}({\mathcal{M}}_B)$. Finally, some applications are given in Gorenstein homological algebra.