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The evolution of electromagnetic and thermodynamic fields in a non-idealfluid are studied in the framework of ultrarelativistic transversemagnetohydrodynamics (MHD), which is essentially characterized by electric andmagnetic fields being transverse to the fluid velocity. Extending the method ofself-similar solutions of relativistic hydrodynamics to the case ofnon-conserved charges, the differential equations of non-ideal transverse MHDare solved, and two novel sets of self-similar solutions are derived. The firstset turns out to be a boost-invariant and exact solution, which ischaracterized by non-rotating electric and magnetic fields. The second set is anon-boost-invariant solution, which is characterized by rotating electric andmagnetic fields. The rotation occurs with increasing rapidity $\eta$, as theangular velocity is defined by$\omega_{0}\equiv\frac{\partial\zeta}{\partial\eta}=\frac{\partial\phi}{\partial\eta}$,with $\zeta$ and $\phi$ being the angles of electric and magnetic vectors withrespect to a certain axis in the local rest frame of the fluid. For both setsof solutions, the electric and magnetic fields are either parallel oranti-parallel to each other. Performing a complete numerical analysis, theeffects of finite electric conductivity as well as electric and magneticsusceptibilities of the medium on the evolution of rotating and non-rotatingMHD solutions are explored, and the interplay between the angular velocity$\omega_{0}$ and these quantities is scrutinized. The lifetime ofelectromagnetic fields and the evolution of the temperature of theelectromagnetized fluid are shown to be affected by $\omega_{0}$.

Novel self-similar rotating solutions of non-ideal transverse magnetohydrodynamics