Related papers: Delta Shock as Free Piston in Pressureless Euler F…
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit the concentration of mass. It is found that, under the requirement of satisfying the…
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…
We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact…
We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…
Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets. For the three-dimensional steady non-isentropic compressible Euler system with frictions, we had constructed a family of transonic shock solutions in…
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…
In this paper, we establish a mathematical theory on statement and validation of the hypersonic similarity law within the framework of Radon measure solutions of steady compressible Euler equations. We consider two scenarios: (1)…
We are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…
Consider a $1$D simple small-amplitude solution $(\rho_{(bkg)}, v^1_{(bkg)})$ to the isentropic compressible Euler equations which has smooth initial data, coincides with a constant state outside a compact set, and forms a shock in finite…
We establish the existence and stability of cylindrical transonic shock solutions under three dimensional perturbations of the incoming flows and the exit pressure without any further restrictions on the background transonic shock…
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importance, their behavior in turbulent regimes remains incompletely…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an $L^\infty$ bound for $C^1$ solutions of the…
We are concerned with a two-dimensional ($2$-D) Riemann problem for compressible flows modeled by the pressure gradient system that is a $2$-D hyperbolic system of conservation laws. The Riemann initial data consist of four constant states…
This paper is concerned with the Riemann problem for the isentropic Chaplygin gas magnetogasdynamics equations and the formation of delta shocks and vacuum states as pressure and magnetic field vanish. Firstly, the Riemann problem of the…
We proposed rigorous definitions of Radon measure solutions for boundary value problems of steady compressible Euler equations which modeling hypersonic-limit inviscid flows passing two-dimensional ramps, and their interactions with still…
The existence and stability of a spherical transonic shock in a hemispherical shell under the three dimensional perturbations of the incoming flows and the exit pressure is established without any further restrictions on the background…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
The one-dimensional piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a dispersive fluid described by the nonlinear Schr\"odinger equation is analyzed.…
When a circular symmetric piston suddenly expands into a still gas, a leading shock wave is generated. This paper investigates an inverse problem of reconstructing the trajectory of the piston from the given leading shock front and the…