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Non-metric two-component Euler equations on the circle

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Abstract

A geometric approach to the study of natural two-component generalizations of the periodic Hunter–Saxton is presented. We give rigorous evidence of the fact that these systems can be realized as geodesic equations with respect to symmetric linear connections on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle \({{\text{\sc Diff}}(\mathbb{S})}\) with the space of smooth functions on the circle. An immediate consequence of this approach is a well-posedness result of the corresponding Cauchy problems in the smooth category.

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Hanover, 30167, Hanover, Germany

    Joachim Escher

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  1. Joachim Escher
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Correspondence to Joachim Escher.

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Communicated by Adrian Constantin.

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Escher, J. Non-metric two-component Euler equations on the circle. Monatsh Math 167, 449–459 (2012). https://doi.org/10.1007/s00605-011-0323-3

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  • DOI: https://doi.org/10.1007/s00605-011-0323-3

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