Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 97, Issue 1, Pages 45-60Publisher
SPRINGER
DOI: 10.1007/s11005-011-0464-2
Keywords
Euler-Poincare equation; homogeneous space; Cauchy problem; well posedness
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Funding
- Fields Institute
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We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar, equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, mu CH and mu DP equations, and the geodesic equations with respect to right-invariant Sobolev metrics on the group of diffeomorphisms of the circle.
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