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 …

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 …

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free
boundary is acted upon by an external pressure posited to be in traveling wave form with a …

In this paper we study solitary traveling wave solutions to a damped shallow water system,
which is in general quasilinear and of mixed type. We develop a small data well-posedness …

We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous
shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond …

We prove that traveling waves in viscous compressible liquids are a generic phenomenon.
The setting for our result is a horizontally infinite, finite depth layer of compressible …