  The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the
Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes
into account contributions from nonlocal damping and is valid at moderate
temperature below the Curie temperature. Therefore, it is used to explain some
discrepancies between the experimental observations and the known theories in
various problems on magnonics and magnetic domain-wall dynamics. In this paper,
the existence and uniqueness of global weak, strong, and regular solutions to
LLBar equation are proven. H\"older continuity of the solution is also
discussed.
