5 papers · 1 filter
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…
Ricci curvature for hydrodynamics on the sphere
Leandro Lichtenfelz, Klas Modin, Stephen C. Preston
The geometric description of incompressible hydrodynamics, as geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms, enables notions of curvature i…
Conjugate points on Lie groups with left-invariant metrics
Alice Le Brigant, Leandro Lichtenfelz, Stephen C. Preston
We prove sufficient conditions for the existence of conjugate points along geodesics of a left-invariant metric on a Lie group, using a reformulation of the index form in terms of…
Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid
Leandro Lichtenfelz, Taito Tauchi, Tsuyoshi Yoneda
The existence of a conjugate point on the volume-preserving diffeomorphism group of a compact Riemannian manifold M is related to the Lagrangian stability of a solution of the inco…
Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds
Leandro Lichtenfelz, Gerard Misiolek, Stephen C. Preston
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fre…