期刊
LETTERS IN MATHEMATICAL PHYSICS
卷 97, 期 1, 页码 45-60出版社
SPRINGER
DOI: 10.1007/s11005-011-0464-2
关键词
Euler-Poincare equation; homogeneous space; Cauchy problem; well posedness
资金
- Fields Institute
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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