32 citations · 135 across the 28 of their papers we have counts for
10 papers · 1 filter
Liouville comparison theory for blowup of Euler-Arnold equations
Martin Bauer, Stephen C. Preston, Justin Valletta
In this article we introduce a new blowup criterion for (generalized) Euler-Arnold equations on . Our method is based on treating the equation in Lagrangian coordinate…
Solar models and McKean's breakdown theorem for the CH and DP equations
Stephen C. Preston
We study the breakdown for CH and DP equations on the circle, given by for , where is the mean and or respect…
Local well-posedness of the Camassa-Holm equation on the real line
Jae Min Lee, Stephen C. Preston
In this paper we prove the local well-posedness of the Camassa-Holm equation on the real line in the space of continuously differentiable diffeomorphisms with an appropriate decayi…
Lagrangian aspects of the axisymmetric Euler equation
Stephen C. Preston, Alejandro Sarria
In this paper we are interested in geometric aspects of blowup in the axisymmetric 3D Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flo…
Geometric investigations of a vorticity model equation
Martin Bauer, Boris Kolev, Stephen C. Preston
This article consists of a detailed geometric study of the one-dimensional vorticity model equation $$ω_{t} + uω_{x} + 2ωu_{x} = 0, \qquad ω= H u_{x}, \qquad t\in\mathbb{R},\; x\in…
Riemannian geometry of the contactomorphism group
David G. Ebin, Stephen C. Preston
We define a right-invariant Riemannian metric on the group of contactomorphisms and study its Euler-Arnold equation. If the metric is associated to the contact form, the Euler-Arno…