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

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