Related papers: Self-similar imploding relativistic shock waves
We solve the continuation problem for the non-isentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar G\"uderley imploding shock solutions for a perfect gas with adiabatic…
We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and specifically the similarity exponent which determines…
Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We…
A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically…
A spherical blast wave with relativistic velocity can be described by a similarity solution, that is used for theoretical models of gamma-ray bursts. We consider the linear stability of such a relativistic blast wave propagating into a…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
Spherical or cylindrical convergent shock waves in imploding materials are one of the most effective ways to produce extremely high pressures, densities and temperatures, hardly attainable in plane shock waves generated by chemical high…
We derive self similar solutions for ultra-relativistic shock waves propagating into cold material of powerlaw density profile in radius rho ~ r^-k. We treat both implosions and explosions in three geometries: planar, cylindrical and…
Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\frac1\ell\varrho$…
We introduce what we call a locally inertial Godunov method with dynamical time dilation, and use it to simulate a new one parameter family of general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The…
Self-similar solution is obtained for propagation of a strong shock, in a flat expanding dusty Friedman universe. Approximate analytic solution was obtained earlier, using relation between self-similar variables, equivalent to the exact…
We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold…
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…
Coughlin et al. (2018) (Paper I) derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low energy explosions,…
We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density…
In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for $\gamma\in (1,3]$. These solutions are analytic away from the shock interface before collapse, and…
We consider the corrugation instability of the self-similar flow with an accelerating shock in the highly relativistic regime. We derive the correct dispersion relation for the proper modes in the self-similar regime, and conclude that this…
A new type of self-similarity is found in the problem of a plane-parallel, ultra-relativistic blast wave, propagating in a powerlaw density profile of the form $\rho \propto z^{-k}$. Self-similar solutions of the first kind can be found for…
The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytrope-like density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic--that…
The solution of self-similar shock dynamics satisfying the inviscid Burgers equation are provided in closed form for planar, cylindrical and spherical problems. The approach follows Lee's method for obtaining self-similar solutions for the…