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The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives asimple description of spin dynamics in the condensate. We introduce thehydrodynamic equation of a ferromagnetic BEC with dissipation originating fromthe energy dissipation of the condensate. The dissipative hydrodynamic equationhas the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, whichdescribes the magnetization dynamics of ferromagnets interacting withspin-polarized currents. Employing the dissipative hydrodynamic equation, wedemonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in thepresence and absence of a current of particles, and discuss the effects of thecurrent on domain pattern formation. We also discuss the characteristic lengthsof domain patterns that have domain walls with and without finitemagnetization.

Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets