AbstractIn two earlier papers (BRÄUER and RÄDLER 1986, 1987) the evolution of a magnetic field was considered which pervades an electrically conducting fluid and its non‐conducting surroundings. A construction principle for Green's functions of the corresponding initial value problem was proposed, and worked out for the case in which the fluid fills a spherical region. Now the principle is applied to the case of a fluid body occupying a half‐space. Green's functions are constructed for arbitrary motions of the fluid. More concrete results are derived for shear flow, and explicit expressions of Green's functions are given for rigid body m