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arXiv · 2312.15019

The uniform existence time and Zero-Alpha limit problem of the Euler-Poincaré equations

Min Li·Zhaoyang Yin
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Abstract

We consider the Cauchy problem of the Euler-Poincaré equations in $\mathbb{R}^d$ with a varying dispersion parameter $α$. Based on the convex entropy structure and the modified commutator estimates, we have proved that the Euler-Poincaré equations have a uniform existence time with respect to $α$ in Sobolev spaces $H^s.$ Combined with the Bona-Simth method, we obtain convergence of the solutions to the Euler-Poincaré equations as $α\to 0$ in the same space where the initial data are located.

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Min Li, Zhaoyang Yin. 2024-06-17. The uniform existence time and Zero-Alpha limit problem of the Euler-Poincaré equations. https://arxiv.org/abs/2312.15019

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