Related papers: A hydrodynamic approach to the classical ideal gas
The presented paper is an attempt to investigate the dynamical states of an hydrodynamical isothermal turbulent self-gravitating system using some powerful tools of the classical thermodynamics. Our main assumption, inspired by the work of…
We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas…
We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes equations, we prove…
We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations,…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
The ideal gas equation of state with a constant adiabatic index, although commonly used in relativistic hydrodynamics, is a poor approximation for most relativistic astrophysical flows. Here we propose a new general equation of state for a…
We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the Third Law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to…
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite…
Lagrangian reduction by stages is used to derive the Euler-Poincar\'e equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous…
We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal…
The purpose of this paper is to present a novel optimal theoretical framework based on potential flow theory in ideal gas dynamics which provides a smooth extrapolation of Parker's steady solar wind model to the unsteady case. The viability…
We are concerned with the one-dimensional piston problem for the compressible Euler equations of Chaplygin gas. If the piston moves at constant subsonic speed to the uniform gas, there exists an integral weak solution for the piston…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler system. Our analysis is based on a 1+3 tetrad formalism which makes use of the components of the Weyl tensor as…
The adiabatic piston problem is solved at the mesoscale using a Kinetic Theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston).…
Following the recent success of anisotropic hydrodynamics we propose a new, general prescription for the hydrodynamics expansion around an anisotropic background. The anisotropic distribution is fixing exactly the complete energy-momentum…
We present a simple, analytic model for the accretion flow of an incompressible wind onto a gravitating object. This solution corresponds to the Newtonian limit of a previously known relativistic model for a fluid obeying a stiff equation…
We investigate here gravitational collapse of a perfect fluid with a linear isentropic equation of state $p = k \rho$. A class of collapse models is given which is a family of solutions to Einstein equations and the final fate of collapse…
A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The…
Abandoning the perfect fluid hypothesis, we investigate here the possibility that the dark energy equation of state (EoS) $w$ is a nonlinear function of the energy density $\rho$. To this aim, we consider four different EoS describing…