4 papers
Exact non-stationary solutions of the Euler equations in two and three dimensions
Patrick Heslin, Stephen C. Preston
We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equa…
Breakdown of smooth solutions to the subcritical EPDiff equation
Martin Bauer, Stephen C. Preston, Justin Valletta
We consider the EPDiff equation on with the integer-order homogeneous Sobolev inertia operator . We prove that for arbitrary radial initial data and a sign…
Zeitlin's model for axisymmetric 3-D Euler equations
Klas Modin, Stephen C. Preston
Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometri…
Geometric Analysis of the Generalized Surface Quasi-Geostrophic Equations
Martin Bauer, Patrick Heslin, Gerard Misiołek +1
We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid surface quasi-geostroph…