  We compute the radius of convergence of the linearized relativistic
hydrodynamic expansion around a non-trivially rotating strongly coupled N=4
Super-Yang-Mills plasma. Our results show that the validity of hydrodynamics is
sustained and can even get enhanced in a highly vortical quark-gluon plasma,
such as the one produced in heavy-ion collisions. The hydrodynamic dispersion
relations are computed using a rotating background that is an analytic solution
of the ideal hydrodynamic equations of motion with non-vanishing angular
momentum and large vorticity gradients, giving rise to a particular boost
symmetry. Analytic equations for the transport coeffcients of the rotating
plasma as a function of their values in a plasma at rest are given.
