Stable models of Lubin-Tate curves with level three

We construct a stable formal model of a Lubin-Tate curve of level three, and study the action of a Weil group and a division algebra on its stable reduction. Further, we study a structure of cohomology of the Lubin-Tate curve. Our study is purely local and includes the case where the characteristic of the residue field of a local field is two.