6 papers · 1 filter
Desingularization of nondegenerate rotating vortex patches
RÄzvan-Octavian Radu, Noah Stevenson
This paper analyzes the space of steady rotating solutions to the two-dimensional incompressible Euler equations nearby vortex patch solutions satisfying a natural nondegeneracy co…
On large periodic traveling surface waves in porous media
Huy Q. Nguyen, Noah Stevenson
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bou…
Gravity driven traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations
Noah Stevenson, Ian Tice
We give the first mathematical construction of two-dimensional traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations for a single finite depth l…
Stationary wave solutions to two dimensional viscous shallow water equations: theory of small and large solutions
Noah Stevenson, Ian Tice
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing…
Periodic gravity-capillary roll wave solutions to the inclined viscous shallow water equations in two dimensions
Noah Stevenson
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…
The traveling wave problem for the shallow water equations: well-posedness and the limits of vanishing viscosity and surface tension
Noah Stevenson, Ian Tice
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…