Related papers: Convergence Rate of Hypersonic Similarity for Stea…
We establish the optimal convergence rate to the hypersonic similarity law, which is also called the Mach number independence principle, for steady compressible full Euler flows over two-dimensional slender Lipschitz wedges. The problem can…
We establish the optimal convergence rate of the hypersonic similarity for two-dimensional steady potential flows with {\it large data} past over a straight wedge in the $BV\cap L^1$ framework, provided that the total variation of the large…
In this paper, we establish the first rigorous mathematical global result on the validation of the hypersonic similarity, which is also called the Mach-number independence principle, for the two dimensional steady potential flow. The…
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 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 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…
In a recent publication Hornung (2019) showed that the shock wave stand-off distance and the drag coefficient of a cone in inviscid hypersonic flow of a perfect gas can be expressed as the product of a function of the inverse normal-shock…
For a supersonic Euler flow past a straight wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the…
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…
In this paper, we study the existence of a global transonic shock generated by hypersonic potential flow over a large curved convex wedge. Modeling 2-dimensional steady potential flow leads to a free boundary value problem of quasilinear…
The nonlinear wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ determines a flow of conservative solutions taking values in the space $H^1(\mathbb{R})$. However, this flow is not continuous w.r.t. the natural $H^1$ distance. Aim of this paper is to…
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…
We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach…
We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of…
The flow field with a Mach number larger than 5 is named hypersonic flow. In this paper, we explore the existence of smooth flow field after shock for hypersonic potential flow past a curved smooth wedge with neither smallness assumption on…
We consider a boundary value problem of a stationary advection equation with the homogeneous inflow boundary condition in a bounded domain with Lipschitz boundary, and consider its perturbation by $\epsilon \Delta$, where $\epsilon$ is a…
Let $\mathbb{H}$ be the sub-Riemannian Heisenberg group. That $\mathbb{H}$ supports a rich family of quasiconformal mappings was demonstrated by Kor\'{a}nyi and Reimann using the so-called flow method. Here we supply further evidence of the…
This study aims to shed light on hypersonic attachment-line instabilities with large sweep Mach numbers. Highly swept flows over a cold cylinder that give rise to large sweep Mach numbers are studied. High fidelity base flows are obtained…
How to determine accurately and efficiently the aerodynamic forces of the aircraft in high-speed flow is one of great challenges in modern aerodynamics. In this Letter we propose a new similarity law for steady transonic-supersonic flow…
In this paper, we study the problem of shock reflection by a wedge, with the potential flow equation, which is a simplification of the Euler System. In the work of M. Feldman and G. Chen, the existence theory of shock reflection problems…