Related papers: Detached shock past a blunt body
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…
A new solution method is presented for steady-state, momentum-conserving, non-axisymmetric bow shocks and colliding winds in the thin-shell limit. This is a generalization of previous formulations to include a density gradient in the…
When a plane shock hits a two-dimensional 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. The experimental, computational,…
I present time-dependent analytical solutions of quasi-steady shocks with cooling, where quasi-steady shocks are objects composed of truncated steady-state models of shocks at any intermediate time. I compare these solutions to simulations…
We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the…
We consider the 3D isentropic compressible Euler equations with the ideal gas law. We provide a constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, with nontrivial vorticity present at…
Under the genuinely nonlinear assumption for 1-D $n\times n$ strictly hyperbolic conservation laws, we investigate the geometric blowup of smooth solutions and the development of singularities when the small initial data fulfill the generic…
We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…
We investigate for a large class of nonlinear wave equations, which allow for shock wave formations, how these solutions behave when they are PT-symmetrically deformed. For real solutions we find that they are transformed into peaked…
Supersonic-sonic patches are ubiquitous in regions of transonic flows and they boil down to a family of degenerate hyperbolic problems in regions surrounded by a streamline, a characteristic curve and a possible sonic curve. This paper…
We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…
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…
We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the…
We study the Cauchy problem for classical and weak shock-forming solutions to a model quasilinear wave equation in $1+1$ dimensions arising from a convenient choice of $C^{\infty}$ initial data, which allows us to solve the equation using…
The stability of an irreversible singularity, such as a Riemann shock to the full Euler system, in the absence of any technical conditions on perturbations, remains a major open problem even within mono-dimensional framework. A natural…
We show that the 1D planar ultrarelativistic shock-tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the…
Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation…
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…
This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…