相关论文: Small viscosity method and criteria for shock wave…
We present a criterion for a shock wave existence in relativistic magnetic hydrodynamics with an arbitrary (possibly non-convex) equation of state. The criterion has the form of algebraic inequality that involves equation of state of the…
We consider an imperfect relativistic fluid which develops a shock wave and discuss its structure and thickness, taking into account the effects of viscosity and heat conduction in the form of sound absorption. The junction conditions and…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge…
We study several mathematical aspects of a system of equations modelling the interaction between short waves, described by a nonlinear Schr\"{o}dinger equation, and long waves, described by the equations of magnetohydrodynamics for a…
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading…
We derive relativistic resistive magnetohydrodynamics for a two-component ultrarelativistic plasma directly from kinetic theory. Starting with the Boltzmann--Vlasov equation and using the 14-moment approximation in the Landau frame, we…
We have applied thermodynamic stability analysis to derive the stability and causality conditions for conventional relativistic viscous hydrodynamics and spin hydrodynamics. We obtain the thermodynamic stability conditions for second-order…
Solutions of shock waves in anisotropic relativistic hydrodynamics in the absence of refraction of the flow passing through the shock wave are considered. The existence of a critical value of the anisotropy parameter is shown. This value is…
We consider a $L^2$-contraction of large viscous shock waves for the multi-dimensional scalar viscous conservation laws, up to a suitable shift. The shift function depends on the time and space variables. It solves a parabolic equation with…
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely…
Shock wave solutions in anisotropic relativistic hydrodynamics are considered. A new phenomenon of anisotropy-related angular deflection of the incident flow by the shock wave front is described. Patterns of velocity and momentum…
We present and test a new, special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived…
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock…
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…
Dissipationless hydrodynamics regularized by dispersion describe a number of physical media including water waves, nonlinear optics, and Bose-Einstein condensates. As in the classical theory of hyperbolic equations where a non-convex flux…
We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare…
We study linearized stability in first-order relativistic viscous hydrodynamics in the most general frame. There is a region in the parameter space of transport coefficients where the perturbations of the equilibrium state are stable. This…
We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' or partial viscosity. The main result is the establishment of…
Starting from kinetic theory description of massive spin-1/2 particles in presence of magnetic field, equations for relativistic dissipative non-resistive magnetohydrodynamics are obtained in the small polarization limit. We use a…