Search Results - "Preston, Stephen C."

Solar models and McKean’s breakdown theorem for the μCH and μDP equations by Preston, Stephen C.

“…We study the breakdown for μ CH and μ DP equations on the circle, given by m t + u m θ + λ u θ m = 0 , for m = μ ( u ) - u θ θ , where μ is the mean and λ = 2…”
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On the volumorphism group, the first conjugate point is always the hardest by PRESTON, Stephen C

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Isometric Immersions and the Waving of Flags by Bauer, Martin, Møller-Andersen, Jakob, Preston, Stephen C.

“…In this article we propose a novel geometric model to study the motion of a physical flag. In our approach, a flag is viewed as an isometric immersion from the…”
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Vanishing Distance Phenomena and the Geometric Approach to SQG by Bauer, Martin, Harms, Philipp, Preston, Stephen C.

“…In this article we study the induced geodesic distance of fractional order Sobolev metrics on the groups of (volume preserving) diffeomorphisms and…”
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Geometric analysis of the generalized surface quasi-geostrophic equations by Bauer, Martin, Heslin, Patrick, Misiołek, Gerard, Preston, Stephen C.

“…We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid…”
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Shape Analysis of Surfaces Using General Elastic Metrics by Su, Zhe, Bauer, Martin, Preston, Stephen C., Laga, Hamid, Klassen, Eric

“…In this article, we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the…”
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Axisymmetric Diffeomorphisms and Ideal Fluids on Riemannian 3-Manifolds by Lichtenfelz, Leandro, Misiołek, Gerard, Preston, Stephen C

“…Abstract We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the $L^2$ exponential map on the group of volume-preserving…”
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Conjugate Points Along Kolmogorov Flows on the Torus by Le Brigant, Alice, Preston, Stephen C.

“…The geodesics in the group of volume-preserving diffeomorphisms (volumorphisms) of a manifold M , for a Riemannian metric defined by the kinetic energy, can be…”
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Geodesic completeness of the H3/2 metric on Diff(S1) by Bauer, Martin, Kolev, Boris, Preston, Stephen C.

“…Of concern is the study of the long-time existence of solutions to the Euler–Arnold equation of the right-invariant H 3 2 -metric on the diffeomorphism group…”
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Fredholm properties of Riemannian exponential maps on diffeomorphism groups by Misiołek, Gerard, Preston, Stephen C.

“…We prove that exponential maps of right-invariant Sobolev H r metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear Fredholm maps of…”
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The Geometry of Axisymmetric Ideal Fluid Flows with Swirl by Washabaugh, Pearce, Preston, Stephen C.

“…The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold M can give information about the stability of inviscid,…”
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The geometry of whips by Preston, Stephen C.

“…In this article, we study geometric aspects of the space of arcs parameterized by unit speed in the L 2 metric. Physically, this corresponds to the motion of a…”
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A Geometric Rigidity Theorem for Hydrodynamical Blowup by Preston, Stephen C.

“…Suppose there is a smooth solution u of the Euler equation on a 3-dimensional manifold M, with Lagrangian flow η, such that for some Lagrangian path η(t, x)…”
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The WKB Method for Conjugate Points in the Volumorphism Group by Preston, Stephen C.

“…Using the fact that ideal fluid flow corresponds to geodesics of a Riemannian metric on the volumorphism group, we show that the location of conjugate points…”
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Conjugate point criteria on the area-preserving diffeomorphism group by Preston, Stephen C.

“…This paper answers some questions about conjugate points along the geodesics corresponding to steady 2D Euler flows, posed by a paper of…”
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Liouville comparison theory for breakdown of Euler-Arnold equations by Bauer, Martin, Preston, Stephen C., Valletta, Justin

“…In this article we study breakdown of solutions for (generalized) Euler-Arnold equations on Rn. Our method is based on treating the equation in Lagrangian…”
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Nonpositive curvature on the area-preserving diffeomorphism group by Preston, Stephen C.

“…A steady ideal fluid flow on a surface corresponds to a geodesic in the area-preserving diffeomorphism group. The sign of the curvature operator along this…”
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Geometric investigations of a vorticity model equation by Bauer, Martin, Kolev, Boris, Preston, Stephen C.

“…This article consists of a detailed geometric study of the one-dimensional vorticity model equationωt+uωx+2ωux=0,ω=Hux,t∈R,x∈S1, which is a particular case of…”
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The motion of whips and chains by Preston, Stephen C.

“…We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations η t t = ∂ s ( σ η s ) , σ s s − |…”
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Geodesic completeness of the $$H^{3/2}$$ metric on $$\mathrm {Diff}(S^{1}) by Bauer, Martin, Kolev, Boris, Preston, Stephen C.

“…Of concern is the study of the long-time existence of solutions to the Euler--Arnold equation of the right-invariant $H^{3/2}$-metric on the diffeomorphism…”
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