3 citations · 3 across the 4 of their papers we have counts for
5 papers
Distance Geometry and a Hydrodynamical Hopf-Rinow Criterion
Theodore D. Drivas, Patrick Heslin, Gerard Misiołek
The hydrodynamical Hopf-Rinow problem asks whether a given reconfiguration of an ideal fluid can be attained by an Euler flow. On the flat two-dimensional torus, we give an equival…
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…
Singular Sets of Riemannian Exponential Maps in Hydrodynamics
James Benn, Patrick Heslin, Leandro Lichtenfelz +1
We prove that the singular sets for the Lagrangian solution maps of the two-dimensional inviscid Euler and generalized surface quasi-geostrophic equations are Gaussian null sets. T…
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…
Completeness and geodesic distance properties for fractional Sobolev metrics on spaces of immersed curves
Martin Bauer, Patrick Heslin, Cy Maor
We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of poss…