48 citations · 207 across the 28 of their papers we have counts for
30 papers
Global bifurcation for steady viscous roll waves on an incline
Daniel Abraham, Miles H. Wheeler
We construct a branch of travelling periodic `roll wave' solutions to the free-boundary incompressible Navier--Stokes equations on an inclined plane in two dimensions. These soluti…
Extreme internal waves: gravity currents and overturning fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
Hydrodynamic bores are front-type traveling wave solutions to the two-layer free boundary Euler equations in two dimensions. The velocity field in each layer is assumed to be incom…
Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
Miles H. Wheeler
In this note we construct smooth bounded domains , other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} Δu + λu &= 0 &\qquad…
Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity
Alex Doak, Karsten Matthies, Jonathan Sewell +1
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity sep…
Finite-time self-similar implosion of hollow vortices
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we consider the finite-time blowup of hollow vortices. These are solutions of the two-dimensional Euler equations for which the fluid domain is the complement of fin…
Overhanging solitary water waves
Juan Dávila, Manuel del Pino, Monica Musso +1
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vo…
Vortex-carrying solitary gravity waves of large amplitude
Robin Ming Chen, Kristoffer Varholm, Samuel Walsh +1
In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensi…
On the vorticity threshold for steady water waves
Evgeniy Lokharu, Miles H. Wheeler
One of the most striking features of two-dimensional steady water waves with adverse vorticity is the emergence of stagnation points in the flow, even along branches of solutions t…
Solitary solutions to the steady Euler equations with piecewise constant vorticity in a channel
Karsten Matthies, Jonathan Sewell, Miles H. Wheeler
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is cont…
Desingularization and global continuation for hollow vortices
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; it can therefore be interpreted as a spinning bubble of air in wate…
Rigidity of three-dimensional internal waves with constant vorticity
Robin Ming Chen, Lili Fan, Samuel Walsh +1
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves benea…
Large-amplitude steady solitary water waves with constant vorticity
Susanna V. Haziot, Miles. H. Wheeler
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works…
Traveling water waves -- the ebb and flow of two centuries
Susanna V. Haziot, Vera Mikyoung Hur, Walter Strauss +4
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characte…
Overhanging and touching waves in constant vorticity flows
Vera Mikyoung Hur, Miles H. Wheeler
We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhang…
Multipole vortex patch equilibria for active scalar equations
Zineb Hassainia, Miles H. Wheeler
We study how a general steady configuration of finitely-many point vortices, with Newtonian interaction or generalized surface quasi-geostrophic interactions, can be desingularized…
Solitary waves in a Whitham equation with small surface tension
Mathew A. Johnson, Tien Truong, Miles H. Wheeler
Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated sol…
Liouville chains: new hybrid vortex equilibria of the 2D Euler equation
Vikas S. Krishnamurthy, Miles H. Wheeler, Darren G. Crowdy +1
A large class of new exact solutions to the steady, incompressible Euler equation on the plane is presented. These hybrid solutions consist of a set of stationary point vortices em…
Global bifurcation of solitary waves for the Whitham equation
Tien Truong, Erik Wahlén, Miles H. Wheeler
The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave problem.…
Global bifurcation of anti-plane shear fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one dir…
Large-amplitude internal fronts in two-fluid systems
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incom…
Global bifurcation for monotone fronts of elliptic equations
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumpt…
Nonexistence of subcritical solitary waves
Vladimir Kozlov, Evgeniy Lokharu, Miles H. Wheeler
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open probl…
Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we present a novel center manifold reduction theorem for quasilinear elliptic equations posed on infinite cylinders. This is done without a phase space in the sense…
When Are There Continuous Choices for the Mean Value Abscissa?
David Lowry-Duda, Miles H. Wheeler
The mean value theorem of calculus states that, given a differentiable function on an interval , there exists at least one mean value abscissa such that the slope o…