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arXiv · 2103.04401

Matched Pair Analysis of Euler-Poincar\'{e} Flow on Hamiltonian Vector Fields

Oğul Esen·Cristina Sardón·Marcin Zajac
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Abstract

In this paper we provide a matched pair decomposition of the space of symmetric contravariant tensors $\mathfrak{T}\mathcal{Q}$. From this procedure two complementary Lie subalgebras of $\mathfrak{T}\mathcal{Q}$ under \textit{mutual} interaction arise. Introducing a lift operator, the matched pair decomposition of the space of Hamiltonian vector fields is determined. According to these realizations, Euler-Poincar\'{e} flows on such spaces are decomposed into two subdynamics: one of which is the Euler--Poincar\'{e} formulation of isentropic fluid flows, and the other one corresponds with Euler--Poincar\'{e} equations on higher order contravariant tensors ($n\geq 2$)

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Oğul Esen, Cristina Sardón, Marcin Zajac. 2021-03-07. Matched Pair Analysis of Euler-Poincar\'{e} Flow on Hamiltonian Vector Fields. https://arxiv.org/abs/2103.04401

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