On the capillary water waves with constant vorticity

This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinearized and written as a quasilinear dispersive system of equations. By using the energy estimate and the Strichartz estimate, we show that for $s>\frac{5}{4}$, the gravity-capillary water wave system with constant vorticity is locally well-posed in ${\mathcal{H}}^s(\mathbb{R})$.