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We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a…

Analysis of PDEs · Mathematics 2015-05-28 Olga Rozanova

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…

General Relativity and Quantum Cosmology · Physics 2021-01-28 G. S. Bisnovatyi-Kogan , S. A. Panafidina

We derive a fully relativistic, self-similar solution to describe the propagation of a shock along an exponentially decreasing atmosphere, in the limit of very large Lorentz factor. We solve the problem in planar symmetry and compute the…

Astrophysics · Physics 2009-11-07 Rosalba Perna , Mario Vietri

A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary…

Solar and Stellar Astrophysics · Physics 2015-05-13 Lisa Holden , Kevin Hoppins , Benjamin Baxter , Marco Fatuzzo

We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as…

High Energy Astrophysical Phenomena · Physics 2015-06-16 Stephen Ro , Christopher D. Matzner

In this paper, power series solutions for strong spherical shocks of time dependent variable energy propagating in a two-phase gas-particle medium are presented taking into consideration the power series solution technique (Sakurai in J…

High Energy Astrophysical Phenomena · Physics 2018-01-19 R. K. Anand

Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows the…

Analysis of PDEs · Mathematics 2019-01-01 Helge Kristian Jenssen , Charis Tsikkou

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow…

Fluid Dynamics · Physics 2017-06-28 A. F. Nowakowski , A. Ballil , F. C. G. A Nicolleau

We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…

Analysis of PDEs · Mathematics 2016-10-05 Jonathan Luk , Jared Speck

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…

Astrophysics · Physics 2009-11-11 Re'em Sari

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…

Materials Science · Physics 2025-02-06 R. K. Anand

The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Ken-ichi Nakao , Yoshiyuki Morisawa

The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening, and eventual overturning of a wave. Using a self-similar description in two space dimensions, we show that the…

Fluid Dynamics · Physics 2017-05-24 J. Eggers , T. Grava , M. A. Herrada , G. Pitton

We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These…

Astrophysics · Physics 2009-11-07 Xiaohu Wang , Abraham Loeb , Eli Waxman

The propagation of a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas under the action of monochromatic radiation with a constant intensity per unit area, which has variable azimuthal and axial components of…

Fluid Dynamics · Physics 2018-07-20 Ruchi Bajargaan , Arvind Patel

[...] We present results for the statistics of thermal gas and the shock wave properties for a large volume simulated with three different cosmological numerical codes: the Eulerian total variations diminishing code TVD, the Eulerian…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-28 F. Vazza , K. Dolag , D. Ryu , G. Brunetti , C. Gheller , H. Kang , C. Pfrommer

We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In \cite{pomeau1987shock}, a self-similarity approach was proposed for infinite total cross section resulting from a…

Mathematical Physics · Physics 2019-12-25 Yves Pomeau , Minh-Binh Tran

We present a mathematical model for the propagation of the shock waves that occur during planetary collisions. Such collisions are thought to occur during the formation of terrestrial planets, and they have the potential to erode the…

Earth and Planetary Astrophysics · Physics 2019-11-19 Almog Yalinewich , Andrey Remorov

We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…

Analysis of PDEs · Mathematics 2020-06-17 Frank Merle , Pierre Raphael , Igor Rodnianski , Jeremie Szeftel

In this paper, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the…

Analysis of PDEs · Mathematics 2023-11-14 Beixiang Fang , Su Jiang , Piye Sun