Global solutions for a one-dimensional problem in conducting fluids

A mathematical model of the motion of conducting fluids is studied in this paper. The dynamics of such fluids is described by the equations of compressible fluids coupled to the Maxwell’s equations. We prove global existence of strong solution for a one-dimensional initial-boundary value problem of this model (plane conducting flows) with general large data.

► A model describing the motion of conducting fluids is studied. ► We consider the effect of the displacement current. ► We obtain global existence of strong solution with general large data. ► The growth condition on the heat conductivity is better than the previous results.