Relativistic viscous hydrodynamics order by order

TL;DR

This paper introduces a systematic order-by-order derivative expansion method for solving relativistic viscous hydrodynamics, exemplified by Bjorken flow, addressing initial conditions and perturbation evolution.

Contribution

It presents a novel approach to solve viscous hydrodynamics iteratively by derivatives, extending ideal hydrodynamics solutions to include viscous corrections.

Findings

Validated the method using Bjorken flow

Demonstrated handling of initial conditions and perturbations

Provided a framework for higher-order viscous corrections

Abstract

In this paper, we propose a method of solving the viscous hydrodynamics order by order in a derivative expansion. In such a method, the zero-order solution is just one of the ideal hydrodynamics. All the other higher order corrections satisfy the same first-order partial differential equations but with different inhomogeneous terms. We take the Bjorken flow as an example to test the validity of our method and present how to deal with the problems about the initial condition and perturbation evolution in our formalism.