Shock propagation and stability in causal dissipative hydrodynamics

TL;DR

This paper investigates shock wave stability in causal dissipative hydrodynamics, revealing that standard viscosity alone is insufficient for stability, and proposing an additional viscosity linked to the coarse-graining scale.

Contribution

It introduces an extra viscosity term related to the coarse-graining scale to stabilize shock solutions in causal dissipative hydrodynamics.

Findings

Standard viscosity does not ensure shock stability.

An additional viscosity related to coarse-graining stabilizes shocks.

The approach improves understanding of dissipative hydrodynamics stability.

Abstract

We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing an additional viscosity which is related to the coarse-graining scale of the theory.