Related papers: Relativistic Mechanics of Continuous Media
Most derivations of acoustic wave equations involve ensuring that causality is satisfied. Here we explore the consequences of also requiring that the medium should be passive. This is a stricter criterion than causality for a linear system…
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a…
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…
This article continues our previous study of generalized Forchheimer flows in heterogeneous porous media. Such flows are used to account for deviations from Darcy's law. In heterogeneous media, the derived nonlinear partial differential…
We derive a relativistic hodograph equation for a two-dimensional stationary isentropic hydrodynamical motion. For the case of stiff matter, when the velocity of sound coincides with the light speed, the singularity in this equation…
We consider a general approach to the theory of continuous media starting from Lagrangian formalism. This formalism which uses the trajectories if constituents of media is very convenient for taking into account different types of…
We present a continuum (i.e., an effective) description of immiscible two-phase flow in porous media characterized by two fields, the pressure and the saturation. Gradients in these two fields are the driving forces that move the immiscible…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
Radiatively-driven transfer flow perpendicular to a luminous disk is examined in the relativistic regime of $(v/c)^2$, taking into account the gravity of the central object. The flow is assumed to be vertical, and the gas pressure as well…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…
The similarity between the energy spectra of relativistic particles and that of quasi-particles in super-conductivity BCS theory makes us conjecture that the relativistic physical vacuum medium as the ground state of the background field is…
We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
An hydrodynamic description of a one-dimensional flow of an ideal Fermi fluid is constructed from a semiclassical approximation. For an initially fully degenerate fluid, Euler and continuity hydrodynamic equations are dual to two uncoupled…
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…