Linearized fluid gravity correspondence: from shear viscosity to all order hydrodynamics

Using fluid gravity correspondence we determine the linearized stress energy tensor of mathcal N 4 super Yang Mills theory at strong coupling with all orders in derivatives of fluid velocity included We find that the dissipative effects are fully encoded in the shear term and a new one which emerges starting from the third order We derive for the first time closed linear holographic RG flow type equations for generalized