Local-in-time existence of free-surface 3D Euler flow with $H^{2+\delta }$ initial vorticity in a neighborhood of the free boundary

Abstract

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_0\in H^{2.5+\delta }$ is such that $\mathrm{curl}{u}_0\in H^{2+\delta }$ in an arbitrarily small neighborhood of the free boundary, and we use Lagrangian approach to derive an a~priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh-Taylor stability condition.

arXiv comment16 pages

References in corpus (1)

• Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary