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We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1-D isentropic Navier-Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable…
We study a class of initial value problems (IVPs) involving perturbations on a density stratified, quiescent, viscous liquid layer with a free-surface. The geometry is a two-dimensional, rectangular configuration taking into account…
The evolution of a supernova remnant in a cloudy medium as a function of the volume filling factor of the clouds is studied in a three-dimensional axially symmetrical model. The model includes the mixing of heavy elements (metals) ejected…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
Using one-dimensional hydrodynamic simulations including interstellar heating, cooling, and thermal conduction, we investigate nonlinear evolution of gas flow across galactic spiral arms. We model the gas as a non-self-gravitating,…
Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial-pole shell thickness differences that are comparable to these bodies' circumference. The rate of topographic evolution depends on…
Supersonic flows are expected to exist in the atmospheres of irradiated exoplanets, but the question of whether shocks develop lingers. Specifically, it reduces to whether continuous flow in a closed loop may become supersonic and if some…
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…
The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity…
In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial…
Cool, dense condensations such as coronal rain and prominences suggest that coronal plasma can undergo runaway radiative cooling. Connecting this behaviour to linear thermal modes requires us to fully understand the deeper connection…
We investigate self-similar magnetohydrodynamic (MHD) processes in an isothermal self-gravitating fluid with a quasi-spherical symmetry and extend the envelope expansion with core collapse (EECC) solutions of Lou & Shen by incorporating a…
This work presents a linear analytical calculation on the stability and evolution of a compressible, viscous self-gravitating (SG) Keplerian disc with both horizontal thermal diffusion and a constant cooling timescale when an axisymmetric…
(Abridged) Ideal hydrodynamic models of the intracluster medium (ICM) in the core regions of galaxy clusters fail to explain both the observed temperature structure of this gas, and the observed morphology of radio-galaxy/ICM interactions.…
Galactic spiral shocks are dominant morphological features and believed to be responsible for substructure formation within spiral arms in disk galaxies. They can also contribute a substantial amount of kinetic energy to the interstellar…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can…
We review recent 3D high resolution numerical HD and MHD studies of a multi-component and multi-phase ISM. The computational grid was chosen large enough in the disk to represent typical ISM gas patterns, and in the halo to include the full…