94 citations · 255 across the 23 of their papers we have counts for
13 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…
Information geometry of diffeomorphism groups
Boris Khesin, Gerard Misiołek, Klas Modin
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s,…
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…
Geometric Hydrodynamics in Open Problems
Boris Khesin, Gerard Misiolek, Alexander Shnirelman
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new construction…
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…
Geometry of the Madelung transform
Boris Khesin, Gerard Misiolek, Klas Modin
The Madelung transform is known to relate Schrödinger-type equations in quantum mechanics and the Euler equations for barotropic-type fluids. We prove that, more generally, the Mad…
Geometric Hydrodynamics via Madelung Transform
Boris Khesin, Gerard Misiolek, Klas Modin
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that s…
The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary
James Benn, Gerard Misiolek, Stephen C. Preston
We prove that the Riemannian exponential map of the right-invariant metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty bou…
Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups
Jonatan Lenells, Gerard Misiolek
We study the family of -connections of Amari-Chentsov on the homogeneous space of diffeomorphisms modulo volume-preserving diffeomorphims of a…
Geometry of diffeomorphism groups, complete integrability and optimal transport
Boris Khesin, Jonatan Lenells, Gerard Misiolek +1
We study the geometry of the space of densities $\VolM$, which is the quotient space $\Diff(M)/\Diff_μ(M)$ of the diffeomorphism group of a compact manifold by the subgroup of…
Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
Boris Khesin, Jonatan Lenells, Gerard Misiolek
We study an equation lying `mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magne…
Shock waves for the Burgers equation and curvatures of diffeomorphism groups
Boris Khesin, Gerard Misiolek
We establish a simple relation between curvatures of the group of volume-preserving diffeomorphisms and the lifespan of potential solutions to the inviscid Burgers equation before…
Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups
Boris Khesin, Gerard Misiolek
In this note we obtain the characterization for asymptotic directions on various subgroups of the diffeomorphism group. We give a simple proof of non-existence of such directions f…