We consider the free boundary problem for a 3-dimensional, incompressible, irrotational
liquid drop of nearly spherical shape with capillarity. We study the problem from scratch …

This paper concerns the construction of traveling wave solutions to the free boundary
incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like …

We establish that solitary stationary waves in three dimensional viscous incompressible
fluids are a general phenomenon and that every such solution is a vanishing wave-speed …

In this paper we study traveling wave solutions to the free boundary incompressible Navier-
Stokes system with generalized Navier-slip conditions. The fluid is assumed to occupy a …

For a natural number m≥2, we study m layers of finite depth, horizontally infinite, viscous,
and incompressible fluid bounded below by a flat rigid bottom. Adjacent layers meet at free …

We construct global curves of rotational traveling wave solutions to the $2 D $ water wave
equations on a compact domain. The real analytic interface is subject to surface tension …

We introduce a scale of anisotropic Sobolev spaces defined through a three-parameter
family of Fourier multipliers and study their functional analytic properties. These spaces arise …

We study capillary-gravity and capillary surface waves for fluid flows governed by Darcy's
law. This includes flows in vertical Hele-Shaw cells and in porous media (the one-phase …

We study the Muskat problem for one fluid in an arbitrary dimension, bounded below by a
flat bed and above by a free boundary given as a graph. In addition to a fixed uniform …

In this work, we construct traveling wave solutions to the two-phase Euler equations,
featuring a vortex sheet at the interface between the two phases. The inner phase exhibits a …