On the volumorphism group, the first conjugate point is always the hardest

DOI10.1007/s00220-006-0070-9zbMath1113.37062OpenAlexW2058451747WikidataQ125262998 ScholiaQ125262998MaRDI QIDQ882975

Stephen C. Preston

Publication date: 31 May 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-006-0070-9

zbMATH Keywords

geodesicvolume-preserving diffeomorphismsexistence of conjugate pointsideal fluid mechanics

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (17)

Existence of a conjugate point in the incompressible Euler flow on an ellipsoid ⋮ Fredholm properties of Riemannian exponential maps on diffeomorphism groups ⋮ The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary ⋮ Geometric investigations of a vorticity model equation ⋮ Conjugate points along Kolmogorov flows on the torus ⋮ Geometric hydrodynamics in open problems ⋮ The geometry of axisymmetric ideal fluid flows with swirl ⋮ Conjugate points on the symplectomorphism group ⋮ The exponential map near conjugate points in 2D hydrodynamics ⋮ Conjugate points in \(\mathcal{D}_\mu^s(S^2)\) ⋮ Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field ⋮ A Geometric Rigidity Theorem for Hydrodynamical Blowup ⋮ Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space? ⋮ Conjugate point criteria on the area-preserving diffeomorphism group ⋮ Geometry of the contactomorphism group ⋮ Fredholm properties of the \(L^2\) exponential map on the symplectomorphism group ⋮ Conjugate and cut points in ideal fluid motion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonpositive curvature on the area-preserving diffeomorphism group
• The dual least action problem for an ideal, incompressible fluid
• Sturmian theory for ordinary differential equations
• Generalized fluid flows, their approximation and applications
• Topological methods in hydrodynamics
• For ideal fluids, Eulerian and Lagrangian instabilities are equivalent
• On the singularities of the exponential map in infinite dimensional Riemannian manifolds
• Singularities of the exponential map on the volume-preserving diffeomorphism group
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Instability criteria for steady flows of a perfect fluid
• Conjugate points in $\mathcal {D}_{\mu }(T^2)$
• Hilbert Manifolds Without Epiconjugate Points

This page was built for publication: On the volumorphism group, the first conjugate point is always the hardest