We review recent progress on the long-time regularity of solutions of the Cauchy problem for
the water waves equations, in two and three dimensions. We begin by introducing the free …

In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler
equations describing the motion of a liquid in an unbounded initial domain with moving …

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 …

Boundary-layer transition is accompanied by a significant increase in skin friction whose
origin is rigorously explained using the stochastic Lagrangian formulation of the Navier …

In this paper we establish the incompressible limit for the compressible free-boundary Euler
equations with surface tension in the case of a liquid. Compared to the case without surface …

We study a fundamental model in fluid mechanics—the 3D gravity water wave equation, in
which an incompressible fluid occupying half the 3D space flows under its own gravity. In …

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 consider the three-dimensional incompressible free-boundary magnetohydrodynamics
(MHD) equations in a bounded domain with surface tension on the boundary. We establish …

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 …