相关论文: Generalized equations of hydrodynamics in fraction…

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the…

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element.…

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional…

We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…

Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…

By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in…

We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the…

We extend our earlier macrostatistical treatment of hydrodynamical fluctuations about nonequilibrium steady states to viscous fluids. Since the scale dependence of the Navier-Stokes equations precludes the applicability of any infinite…

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the…

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the…

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…

Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the…

In this paper, we derive the Euler and Navier-Stokes equations for electronic two-band systems in arbitrary dimension and with generic power-law dispersion relations. We focus on the hydrodynamic transport regime, where such systems offer a…

The stochastic variational method is applied to particle systems and continuum mediums. As the brief review of this method, we first discuss the application to particle Lagrangians and derive a diffusion-type equation and the…

A new system of general Navier-Stokes-like equations is proposed to model electromagnetic analogous to hydrodynamic. While most attempts to derive analogues of hydrodynamic to electromagnetic, and vice-versa, start with Navier-Stokes or a…

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlin- ear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear…

We show that a Galilean invariant version of fluid dynamics can be derived by the methods of statistical dynamics using Maxwell's balance equations. The basic equation is non-local, and might replace Boltzmann's equation if the latter turns…

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy functionals with a single parameter $q$. These reduce to the extensive Boltzmann-Gibbs form for $q=1$, but…

Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium…