We consider the three-dimensional Euler equations in a domain with a free boundary with
no surface tension. In the Lagrangian setting, we construct a unique local-in-time solution for …

We study several different aspects of the energy equipartition principle for water waves. We
prove a virial identity that implies that the potential energy is equal, on average, to a …

We consider the three-dimensional incompressible magnetohydrodynamics (MHD)
equations in a bounded domain with small volume and free moving surface boundary. We …

A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler
Equation with Surface Tension Page 1 Copyright © by SIAM. Unauthorized reproduction of …

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 …

We derive a priori estimates for the incompressible free-boundary Euler equations with
surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide …

We address the existence of solutions for the free-surface Euler equation with surface
tension in a bounded domain. Considering the problem in Lagrangian variables we provide …

We show that the gravity water waves system is locally wellposed in weighted Sobolev
spaces which allow for interfaces with corners. No symmetry assumptions are required …

We derive a priori estimates for the compressible free-boundary Euler equations with
surface tension in three spatial dimensions in the case of a liquid. These are estimates for …

We consider incompressible inviscid elastodynamics equations with a free surface and
establish regularity of solutions for these equations. Compared with previous result on this …