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The fluid-dynamical modeling of a nuclear collision at high energy usually starts shortly after the collision. A major source of uncertainty comes from the detailed modeling of the initial state. While the collision itself likely involves far-from-equilibrium dynamics, it is not excluded that a fluid theory of second order can reasonably well describe its soft features. Here we explore this possibility and discuss how the state before the collision can be described in that setup, what are the requirements from relativistic causality to the form of the equations of motion, how much entropy production can result from shear and bulk viscous dissipation during the initial longitudinal dynamics, and how one can thus obtain sensible initial conditions for the subsequent transverse expansion. While we do here only first steps, we outline a larger program. If the latter could be successfully completed it could lead to a dynamical description of heavy-ion collisions where the only uncertainty lies in the thermodynamic and transport properties of quantum chromodynamics., Comment: 19 pages, 13 figures

Heavy quarks (i.e. charm and beauty) in heavy-ion collisions are initially produced out of kinetic equilibrium via hard partonic scattering processes. However, recent measurements of anisotropic flow of charmed hadrons pose the question regarding the thermalization of heavy quarks in the quark-gluon plasma (QGP). Exploiting a mapping between transport theory and fluid dynamics, we develop a fluid-dynamic description for charm quarks and show results for charm-hadron momentum distributions. Inspired by recent Lattice-QCD (LQCD) calculations, we show that a late hydrodynamization within the lifetime of the QGP is possible also for beauty quarks., Comment: 4 pages, 2 figures, Contribution to Quark Matter 2023. arXiv admin note: substantial text overlap with arXiv:2307.15580

Exploiting a mapping between transport theory and fluid dynamics, we show how a fluid-dynamic description of the diffusion of charm quarks in the QCD plasma is feasible. We show results for spectra of charmed hadrons obtained with a fluid-dynamic description of the quark-gluon plasma (QGP) coupled with the conservation of a heavy-quark - antiquark current. We compare our calculations with the most recent experimental data in order to provide further constraints on the transport coefficients of the QGP., Comment: Hard Probes 2023

A fluid-dynamic approach to charm-quark diffusion in the quark-gluon plasma (QGP) is developed for the first time. Results for integrated yields and momentum distributions of charmed hadrons obtained with a fluid-dynamic description for the dynamics of the QGP coupled to an additional heavy-quark-antiquark current are shown. In addition to the thermodynamic Equation of State (EoS), this description uses a heavy-quark diffusion constant which we take from Lattice QCD calculations. The results describe quantitatively experimental data measured at the LHC at the center-of-mass energy of $\sqrt{s_{\rm NN}}$ = 5.02 TeV up to $p_{\rm T}\sim$ 4-5 GeV/$c$, showing that charm quarks undergo a very fast hydrodynamization in the medium created by ultrarelativistic heavy-ion collisions., Comment: 11 pages, 6 figures