New, spherical solutions of non-relativistic, dissipative hydrodynamics
G\'abor Kasza (1, 2, 3), L\'aszl\'o Csernai (4, 5), Tam\'as, Cs\"org\H{o} (1, 2) ((1) Wigner RCP, H-1525 Budapest 114, POB 49, Hungary,, (2) MATE Institute of Technology KRC, H-3200 Gy\"ongy\"os, M\'atrai \'ut 36,, Hungary, (3) E\"otv\"os Lor\'and University, H-1118 Budapest XI
TL;DR
This paper introduces a new family of exact, spherically symmetric solutions to non-relativistic dissipative hydrodynamics, revealing that these solutions become asymptotically perfect despite dissipation.
Contribution
The paper presents a novel set of exact solutions for dissipative hydrodynamics with arbitrary viscosities, emphasizing their spherical symmetry and asymptotic perfect fluid behavior.
Findings
Solutions are exact and spherically symmetric.
Dissipative solutions become asymptotically perfect.
Applicable in non-relativistic hydrodynamics with arbitrary viscosities.
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 could draw a surprising conclusion: this new class of exact solutions of non-relativistic dissipative hydrodynamics is asymptotically perfect.
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