1+1 dimensional relativistic viscous non-resistive magnetohydrodynamics with longitudinal boost invariance*

Abstract We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and a shear stress tensor. Several analytical solutions describing the fluid temperature evolution under a given equation of state (EoS) are derived. Extending the Victor-Bjorken ideal MHD flow to include non-zero shear viscosity, we first obtain two perturbative analytical solutions for the first-order (Navier-Stokes) approximation. For small, power-law evolving external magnetic fields, our stable solutions show that both magnetic field and shear viscosity cause fluid heating with an early temperature peak, consistent with numerical results. In the second-order (Israel-Stewart) theory, our numerical results show that the combined presence of magnetic field and shear viscosity leads to a slow cooling rate of fluid temperature, with initial shear stress significantly influencing temperature evolution of the medium.