Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in bounded domain

Yi Wang; Bijun Zuo

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arXiv · 1811.00411

Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in bounded domain

Yi Wang·Bijun Zuo

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Abstract

In this paper, we prove the energy and cross-helicity conservation of weak solutions to the three-dimensional ideal MHD equations in bounded domain under the interior Besov regularity conditions which are exactly same as the three-dimensional periodic domain case in \cite{Caflisch 97}, and the boundedness and the Besov-type continuity for both the velocity and magnetic fields near the boundary, which seem crucial for the bounded domain case due to the boundary effect. Note that the Besov-type continuity condition near the boundary is consistent with the interior Besov regularity, which is a new condition we proposed in the present paper.

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Yi Wang, Bijun Zuo. 2018-11-01. Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in bounded domain. https://arxiv.org/abs/1811.00411

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