Related papers: Supersonic flows with a contact discontinuity to t…
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…
The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit…
This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the…
We are concerned with the existence and compactness of entropy solutions of the compressible Euler system for two-dimensional steady potential flow around an obstacle for a polytropic gas with supersonic far-field velocity. The existence…
We prove the stability of contact discontinuities without shear, a family of special discontinuous solutions for the three-dimensional full Euler systems, in the class of vanishing dissipation limits of the corresponding…
In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points…
The 3D incompressible Euler equation is an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or…
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…
We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than…
We consider a supersonic flow past an airfoil in the context of the steady, isentropic and irrotational compressible Euler equations. We show that for appropriate data, either a shock forms, in which case certain derivatives of the solution…
In this paper, we are trying to show the uniqueness of transonic shock solutions in an expanding nozzle under certain conditions and assumptions on the boundary data and the shock solution. The idea is to compare two transonic shock…
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…
In this paper, by considering the anhedral angle, we for the first time study the problem of supersonic flow of a Chaplygin gas over a conical wing with $\Lambda$-shaped cross sections, where the flow is governed by the three-dimensional…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
The linear stability of rectilinear compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary and the boundary is characteristic. A necessary and sufficient condition is obtained…
We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non-contractible streamlines which foliate the domain), then they must be either parallel or…
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…
In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary…
In this paper, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem modeling isentropic supersonic flows through divergent ducts. The governing equations are the…