Related papers: Revisiting the Strong Shock Problem: Converging an…
In this work we present a mathematical model for the propagation of the shock waves that occur in graded density profiles. These waves can occur in a wide range of astrophysical events, such as collisions in planetary and stellar…
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…
Relativistic collisionless shocks are associated with efficient particle acceleration when propagating into weakly magnetized homogeneous media; as the magnetization increases, particle acceleration becomes suppressed. We demonstrate that…
We investigate shock waves in the unitary Fermi gas by using the zero-temperature equations of superfluid hydrodynamics. We obtain analytical solutions for the dynamics of a localized perturbation of the uniform gas. These supersonic bright…
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…
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…
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…
Non-relativistic collisionless shock waves are widespread in space and astrophysical plasmas and are known as efficient particle accelerators. However, our understanding of collisionless shocks, including their structure and the mechanisms…
We consider ballistic aggregation equation for gases in which each particle is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as…
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…
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,…
The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based…
Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly…
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…
We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney (BBM) and Boussinesq equations. An expansion shock exhibits…
As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is…
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 research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters…
We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and…