11 papers · 1 filter
Smooth and swirling steady vortex rings near the Hill--Norbury family
Răzvan-Octavian Radu, Noah Stevenson
An investigation of local aspects of the space of axisymmetric traveling-wave solutions to the three-dimensional Euler equations near Hill's zero-flux spherical vortex and Norbury'…
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…
Desingularization of nondegenerate rotating vortex patches
Răzvan-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…
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…
Well-posedness of the stationary and slowly traveling wave problems for the free boundary incompressible Navier-Stokes equations
Noah Stevenson, Ian Tice
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit…
Well-posedness of the traveling wave problem for the free boundary compressible Navier-Stokes equations
Noah Stevenson, Ian Tice
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, b…
Traveling wave solutions to the multilayer free boundary incompressible Navier-Stokes equations
Noah Stevenson, Ian Tice
For a natural number , we study layers of finite depth, horizontally infinite, viscous, and incompressible fluid bounded below by a flat rigid bottom. Adjacent layers…
Analysis of micropolar fluids: existence of potential microflow solutions, nearby global well-posedness, and asymptotic stability
Noah Stevenson, Ian Tice
In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists…