Appears in collection : Summer School 2023 - New trends in mathematical fluid dynamics

We prove the local well-posedness of the water waves problem in a 2D domain with contact angles and surface tension. The geometric formulation by Shatah-Zeng is used and adapted here to our case. The contact angle is between $(0, \pi/2)$ and the singularities from related elliptic systems are considered. This talk is based on joint works with Chao Wang.