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 shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of state (EoS) $\varepsilon=3p$ are derived, relevant to relativistic heavy-ion collisions. Extending the Victor-Bjorken ideal MHD flow to include non-zero shear viscosity, two perturbative analytical solutions for the first-order (Navier-Stokes) approximation are obtained. For small, power-law evolving external magnetic fields, our solutions are stable and show that both magnetic field and shear viscosity cause fluid heating with an early temperature peak, align with the numerical results. In the second-order (Israel-Stewart) theory, our findings 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 affecting temperature evolution of QGP.