On the Local Existence and Uniqueness for the 3D Euler Equation with a Free Interface

We address the local existence and uniqueness of solutions for the 3D Euler equations with a free interface. We prove the local well-posedness in the rotational case when the initial datum $$u_0$$ satisfies $$u_0\in H^{2.5+\delta }$$ and , where $$\delta >0$$ is arbitrarily small, under the Taylor condition on the pressure.