Global existence and exponential stability for a 1D compressible and radiative MHD flow (Q439109)

The authors study the boundary-value problem for the system of equations describing the one-dimensional flow of a compressible viscous fluid conductor of electricity in a magnetic field with radiation. Velocity and density are interacting with transverse velocity and magnetic field, changing the total energy and temperature. The domain is a segment, the boundary conditions are homogenous. Global existence and exponential stability of solutions in the Sobolev spaces are established, with some additional properties of the solutions (especially positiveness). The main difficulty is the higher order of nonlinearity with respect to temperature, which demands rather careful estimations.