Euler-Poincaré equations on semi-direct products

DOI10.1007/s00605-014-0720-5zbMath1344.58005OpenAlexW2013054134MaRDI QIDQ264049

Emanuel-Ciprian Cismas

Publication date: 5 April 2016

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-014-0720-5

zbMATH Keywords

Euler-Poincaré equationsdiffeomorphism group of the circlesemi-direct products

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Group structures and generalizations on infinite-dimensional manifolds (58B25)

Related Items

Euler-Poincaré-Arnold equations on semi-direct products. II ⋮ A Nash-Moser approach for the Euler-Arnold equations ⋮ BMS₃invariant fluid dynamics at null infinity

Cites Work

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• Euler equations on a semi-direct product of the diffeomorphisms group by itself
• Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications
• The Degasperis-Procesi equation as a non-metric Euler equation
• Hamiltonian reduction by stages
• Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
• On isomorphic classical diffeomorphism groups. II
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Geodesic flow on the diffeomorphism group of the circle
• Euler equations on homogeneous spaces and Virasoro orbits
• The geometry of a vorticity model equation
• Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
• Continuity of discrete homomorphisms of diffeomorphism groups
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• RESTRICTIONS ON THE GEOMETRY OF THE PERIODIC VORTICITY EQUATION
• On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric
• The Hunter–Saxton Equation: A Geometric Approach
• Isomorphisms between diffeomorphism groups
• Numerical Invariants for Semiconjugacy of Homeomorphisms of the Circle
• On Isomorphic Classical Diffeomorphism Groups. I
• The inverse function theorem of Nash and Moser
• Isomorphisms Between Groups of Diffeomorphisms
• On the geometric approach to the motion of inertial mechanical systems
• Lie Groups and Mechanics: An Introduction
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Geometrical Methods for Equations of Hydrodynamical Type