Related papers: Supersonic flow of a Chaplygin gas past a conical …
In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under…
We consider the problem of supersonic flow of a Chaplygin gas past a delta wing with a shock or rarefaction wave attached to the leading edges. The flow under study is described by the three-dimensional steady Euler system. In conical…
We consider two-dimensional Riemann boundary value problems of Euler equations for the Chaplygin gas with two piecewise constant initial data outside a convex cornered wedge. In self-similar coordinates, when the flow at the wedge corner is…
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 work we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow…
We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the…
We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…
We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken…
We consider the problem of uniform steady supersonic Euler flows passing a straight conical body with attack angles, and study Radon measure solutions describing the infinite-thin shock layers, particularly for the Chaplygin gas and…
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schr\"odinger (NLS) equation. This problem is of fundamental importance as a dispersive…
We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic…
For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such…
We establish the global existence and stability of a three-dimensional supersonic conic shock wave for a perturbed steady supersonic flow past an infinitely long circular cone with a sharp angle. The flow is described by a 3-D steady…
We are concerned with inverse problems for supersonic potential flows past infinite axisymmetric Lipschitz cones. The supersonic flows under consideration are governed by the steady isentropic Euler equations for axisymmetric potential…
In this paper, we prove the unique existence of three-dimensional supersonic solutions to the steady Euler-Poisson system in cylindrical nozzles when prescribing the velocity, entropy, and the strength of electric field at the entrance. We…
This paper concerns supersonic flows with nonzero vorticity governed by the steady Euler-Poisson system, under the coupled effects of the electric potential and the geometry of a convergent nozzle. By the coordinate rotation, the existence…
In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…
We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities,…
In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…
In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…