Various links connecting well-known hydrodynamic chains and corresponding 2+1 nonlinear equations are described.

The closure problem of the stellar hydrodynamic equations is studied in a general case by describing the family of phase space density functions for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. The method is based on the use of maximum entropy distributions, which are afterwards generalised to phase space density functions depending o...

Lattice Boltzmann equations for the isothermal Navier-Stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory. Applied to the shallow water equations, with its different equation of state, the same approach yields discrete equilibria that are subject to a grid scale computational instability....

Based on the generalized kinetic equation for the one-particle distribution function with a small source, the transition from the kinetic to the hydrodynamic description of many-particle systems is performed. The basic feature of this interesting technique to obtain the hydrodynamic limit is that the latter has been partially incorporated into the kinetic equation itself. The hydrodynamic equat...

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the ‘‘fractional’’ continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier–Stokes and Euler equations are considered. We derive the eq...

We show that the boost-invariant and cylindrically asymmetric hydro-dynamic equations for baryon-free matter may be rewritten as only two coupled partial differential equations. In the case where the system exhibits the cross-over phase transition, the standard numerical methods may be applied to solve these equations. An example of our results describing non-central gold on gold collisions at ...