Applied Mathematics and Optimization, Vol.76, No.3, 535-563, 2017
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) is an element of H2.5+delta and u(0) is an element of H2+delta, where delta > 0 is arbitrarily small, under the Taylor condition on the pressure.