Euler-Poincaré-Arnold equations on semi-direct products II

Emanuel-Ciprian  Cismas

doi:10.3934/dcds.2016063

Article Contents

2016, Volume 36, Issue 11: 5993-6022. Doi: 10.3934/dcds.2016063

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Euler-Poincaré-Arnold equations on semi-direct products II

Emanuel-Ciprian Cismas^1,

1.
Institute for Applied Mathematics, Leibniz University, Hannover, Welfengarten 1, 30167

Received: November 30, 2015

Revised: May 31, 2016

Published: May 2017

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Abstract

We study the well-posedness of the Euler-Poincaré-Arnold equations on the semi-direct products of the group of orientation-preserving diffeomorphisms of the circle with itself. To achieve this goal, according to the previous results obtained in [5], we had to extend the results obtained in [10] for the general case of inertia operators of pseudo-differential type.

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Mathematics Subject Classification: Primary: 58D05, 58B25, 22E65; Secondary: 35Q35.

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