New, Spherical Solutions of Non-Relativistic, Dissipative Hydrodynamics

Entropy (Basel). 2022 Apr 6;24(4):514. doi: 10.3390/e24040514.

Abstract

We present a new family of exact solutions of dissipative fireball hydrodynamics for arbitrary bulk and shear viscosities. The main property of these solutions is a spherically symmetric, Hubble flow field. The motivation of this paper is mostly academic: we apply non-relativistic kinematics for simplicity and clarity. In this limiting case, the theory is particularly clear: the non-relativistic Navier-Stokes equations describe the dissipation in a well-understood manner. From the asymptotic analysis of our new exact solutions of dissipative fireball hydrodynamics, we can draw a surprising conclusion: this new class of exact solutions of non-relativistic dissipative hydrodynamics is asymptotically perfect.

Keywords: exact solutions; hydrodynamics; speed of sound; viscosity.