Related papers: Generalized relativistic hydrodynamics with a conv…
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we…
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena…
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
A generalized hydrodynamic theory that systematically incorporates elasticity and viscoelasticity had been derived about a quarter of a century ago. It is based on a strictly Euler point of view, as is natural for hydrodynamics. We used and…
In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
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…
We study solutions of the relativistic hydrodynamical equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions, which describe asymptotic behavior of…
This note presents Godunov variables and 4-potentials for the relativistic Euler equations of barotropic fluids. The associated additional conservation/ production law has different interpretations for different fluids. In particular it…
The formulation of a universal theory for bulk viscosity and heat conduction represents a theoretical challenge for our understanding of relativistic fluid dynamics. Recently, it has been shown that the multifluid variational approach…
We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on…
A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can…
We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…
This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
We cast the non--isentropic relativistic Euler system into a symmetric hyperbolic form. Such systems are very suited to treat initial value problems of hyperbolic type. We obtain this form by using the pressure $p$ and not the density…
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…
We formulate a relativistic hydrodynamic theory for fluids with spin and intrinsic dilation charges. Using an entropy-current analysis, we derive constitutive relations featuring a bulk viscosity and a dilation conductivity governing the…
We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…
We summarize the key ingredients of the recently proposed formalism of relativistic perfect-fluid hydrodynamics with spin. Based on the underlying kinetic theory definitions for the equilibrium distribution functions we obtain the evolution…