Homotopy equivalences and Grothendieck duality over rings with finite Gorenstein weak global dimension

Let $R$ be a ring with Gwgldim$(R)<\mathrm{\infty }$. We obtain a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{G}\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{j})\simeq \mathrm{K}(R\text{-}\mathrm{G}\mathrm{I}\mathrm{n}\mathrm{j})$ which restricts to a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{j})$ $\simeq \mathrm{K}(R\text{-}\mathrm{I}\mathrm{n}\mathrm{j})$. This class of rings includes, among others, (left) Gorenstein rings, Ding-Chen rings and the more general Gorenstein $n$-coherent rings ($n\in \mathbb{N}\cup \{\mathrm{\infty }\},n\ge 2$). As application, we establish some triangle-equivalences of Grothendieck duality over Ding-Chen rings and Gorenstein $n$-coherent rings.