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We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex…
The TOV equations govern the radial evolution of pressure and energy density in static neutron stars (NSs) in hydrodynamical equilibrium. Using the reduced pressure and energy density with respect to the NS central energy density, the…
We present results of numerical modeling made for the galactic stellar and stellar-gas disk embedded in the spherical halo and bulge. The stellar disk is simulated by N-body system, the equations of hydrodynamics are solved by TVD-method.…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
We study the statistical mechanics of classical self-gravitating systems confined within a box of radius $R$ in general relativity. It has been found that the caloric curve $T_{\infty}(E)$ has the form of a double spiral whose shape depends…
First, we construct the Taub-NUT/bolt solutions of $(2k+2)$-dimensinal Einstein-Maxwell gravity, when all the factor spaces of $2k$-dimensional base space $\mathcal{B}$ have positive curvature. These solutions depend on two extra…
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importance, their behavior in turbulent regimes remains incompletely…
Propagation of strong shock wave in the expanding universe is studied using approximate analytic, and exact numerical solution of self-similar equations. Both solutions have similar properties, which change qualitatively, depending on the…
We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the…
In this article, we present a description of the behaviour of shock-compressed solid materials following the Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have…
We performed highly resolved one-dimensional fully compressible Navier-Stokes simulations of heat-release-induced compression waves in near-critical CO2. The computational setup, inspired by the experimental setup of Miura et al., Phys.…
A forced solution $v$ of the Navier-Stokes equation in any open domain with no slip boundary condition is constructed. The scaling factor of the forcing term is the critical order $-2$. The velocity, which is smooth until its final blow up…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
Tensor-scalar theory of gravity allows the generation of gravitational waves from astrophysical sources, like Supernov\ae{}, even in the spherical case. That motivated us to study the collapse of a degenerate stellar core, within…
The hydrodynamics for a gas of hard-spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy $\Delta $ is investigated with the goal of understanding the coupling…
Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work…
The long-time large-distance behaviour of free decaying two dimensional turbulence is studied. Stochastic solutions of the Navier-Stokes equation are explicitly shown to follow renormalisation group trajectories. It is proven that solutions…
Using high-resolution, three-dimensional hydrodynamical simulations, we investigate the structure of the interstellar medium in the central hundred pc region in galaxies, taking into account self-gravity of the gas, radiative cooling from…
The class of scalar-tensor theories with the scalar field coupling to the Gauss-Bonnet invariant has drawn great interest since solutions of spontaneous scalarization were found for black holes in these theories. We contribute to the…
We study the propagation of a Newtonian shock in a spherically symmetric, homologously expanding ejecta. We focus on media with a steep power-law density profile of the form $\rho \propto t^{-3}v^{-\alpha}$, with $\alpha>5$, where $v$ is…