In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of
heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $tau$ is the same as for the time-honored Bjorken flow without magnetic field. Furthermore, when the magnetic field is assumed to decay $sim tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
We investigate the shear viscosity $eta$ and the entropy density $s$ of strongly coupled $mathcal{N}=4$ super Yang-Mills (SYM) plasma in late time of hydrodynamic evolution with AdS/CFT duality and Bjorken scaling. We use correlation function method
proposed by Kovtun, Son and Starinets. We obtain the metric $g_{mu u}$ in a proper time dependent $AdS_{5}$ space through holographic renormalization, whose boundary condition is given by energy-momentum tensor of the plasma in 2+1 dimension with transverse expansion or radial flow. With the metric we compute $eta$ and $s$ of fluids in 1+1 and 2+1 dimension without and with radial flow. We find the ratio $eta/s=1/(4pi)$ in 1+1 dimension consistent with the Kovtun-Son-Starinets bound if next-to-leading terms in proper time are included in the equation of motion for metric perturbations. For 2+1 dimension the result is unchanged in the leading order of transverse rapidity.
