Abstract
In this paper, we prove the energy and cross-helicity conservation of weak solutions to the three-dimensional ideal MHD equations in a bounded domain under the interior Besov regularity conditions which are exactly same as the three-dimensional periodic domain case in [3], and the boundedness and the Besov-type continuity conditions 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 our Besov-type continuity conditions near the boundary are consistent with the interior Besov regularity conditions.
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