The new exact solution of the compressible 3D Navier-Stokes (NS) equations in the case of
zero shear viscosity η= 0 and finite volume viscosityςis obtained. It gives the possibility to …

For the first time the exact strong solution of the three-dimensional (3D) compressible Euler–
Helmholtz (EH) vortex equation in unbounded space is obtained. It corresponds to the …

We study in this work steady laminar flows in a low-density granular gas modelled as a
system of identical smooth hard spheres that collide inelastically. The system is excited by …

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters
only due to dissipative interactions. Here we show that the evolution of a dilute, freely …

Energy dissipation is one of the most important properties of granular gas, which makes its
behavior different from that of molecular gas. In this work we report our investigations on the …

We study the statistics of fluid (gas) density and concentration of passive tracer particles
(dust) in compressible turbulence. As Ma increases from small or moderate values, the …

For the first time the exact vortex solution of the Cauchy problem in unbounded space is
obtained for the three-dimensional Euler-Helmholtz (EH) equation in the case of a nonzero …

In this article we investigate the long-time behavior of the solutions to the energy-dependent,
spatially homogeneous, inelastic Boltzmann equation for hard spheres. This model …

We study closed dense collections of freely cooling hard spheres that collide inelastically
with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the …

The general exact solution of the Cauchy problem to the 3D Euler vortex equation for
compressible flow in unbound space is obtained. This solution has singularity at finite time …