#### Filter Results:

- Full text PDF available (18)

#### Publication Year

1998

2019

- This year (5)
- Last 5 years (17)
- Last 10 years (31)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

Abstract This article consists of a detailed geometric study of the one-dimensional vorticity model equation ω t + u ω x + 2 ω u x = 0 , ω = H u x , t ∈ R , x ∈ S 1 , which is a particular case of… (More)

We prove that exponential maps of right-invariant Sobolev Hr metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear Fredholm maps of index zero as long as r is sufficiently… (More)

Let M be a compact, oriented Riemannian manifold of dimension n, possibly with smooth boundary ∂M . Let D μ(M) denote the group of all diffeomorphisms of Sobolev class H preserving the volume form μ… (More)

Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these… (More)

The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold M can give information about the stability of inviscid, incompressible fluid flows on M. We demonstrate… (More)

In this thesis, we study stability of inviscid fluids in the Lagrangian sense. That is, we look at how paths of particles diverge from each other under a small perturbation of the initial velocity… (More)

- Brad Timerson, Josef Ďurech, +30 authors William F. Thomas
- 2011

No Abstract..

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) and some time T, we have . Then in… (More)

In this paper we prove that all initially-smooth solutions of the Euler-Weil-Petersson equation, which describes geodesics on the universal Teichm\"uller space under the Weil-Petersson metric, will… (More)