Related papers: Solutions of the imploding shock problem in a medi…
We study the Riemann problem for the isentropic compressible Euler equations in two space dimensions with the pressure law describing the Chaplygin gas. It is well known that there are Riemann initial data for which the 1D Riemann problem…
When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis…
The selfconsistent steady state solution for a strong shock, significantly modified by accelerated particles is obtained on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated…
We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form)…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
Although local existence of multidimensional shock waves has been established in some fundamental references, there are few results on the global existence of those waves except the ones for the unsteady potential flow equations in…
We address the problem of shock induced ignition and transition to detonation in a reactive medium in the presence of mechanically induced fluctuations by a moving oscillating piston. For the inert problem prior to ignition, we provide a…
The Euler equations of ideal gas dynamics posess a remarkable nonlinear involutional symmetry which allows one to factor out an arbitrary uniform expansion or contraction of the system. The nature of this symmetry (called by cosmologists…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
We describe the results of 3D simulations of the interaction of hydrodynamic shocks with Bonnor-Ebert spheres performed with an Adaptive Mesh Refinement code. The calculations are isothermal and the clouds are embedded in a medium in which…
One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian approach are performed to investigate the interactions between propagating shock waves and dispersed evaporating water droplets in two-phase gas-droplet flows.…
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction…
Shocks in granular media, such as vertically oscillated beds, have been shown to develop instabilities. Similar jet formation has been observed in explosively dispersed granular media. Our previous work addressed this instability by…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, F. M. Huang, A. Matsumura and X. D. Shi showed that there exists viscous shock wave solution to the inflow…
The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are assumed to be varying according to the power…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…