相关论文: Loss of Regularity of Solutions to Shock Reflectio…

We are concerned with the suitability of the main models of compressible fluid dynamics for the Lighthill problem for shock diffraction by a convex corned wedge, by studying the regularity of solutions of the problem, which can be…

When a plane shock hits a 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. Experimental, computational, and asymptotic analysis…

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a…

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,…

The shock reflection problem is one of the most important problems in mathematical fluid dynamics, since this problem not only arises in many important physical situations but also is fundamental for the theory of multidimensional…

Reflection of a shock from a solid wedge is a classical problem in gas dynamics. Depending on the parameters either a regular or a irregular (Mach-type) reflection results. We construct regular reflection as an exact self-similar solution…

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…

Shock waves are steep wave fronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how…

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of…

Shock waves are fundamental in nature. One of the most fundamental problems in fluid mechanics is shock reflection-diffraction by wedges. The complexity of reflection-diffraction configurations was first reported by Ernst Mach in 1878. The…

We are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and…

We are concerned with the low regularity of self-similar solutions of two-dimensional Riemann problems for the isentropic Euler system. We establish a general framework for the analysis of the local regularity of such solutions for a class…

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…

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…

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…

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the…

Using the standard symmetry technique for applying boundary conditions for free slip and flat walls with corners will lead to flow leak through the wall near corners (violation of no penetration condition) and a corresponding error in…

This paper investigates an incompressible steady free boundary problem of Euler equations with helical symmetry in $3$ dimensions and with nontrivial vorticity. The velocity field of the fluid arises from the spiral of its velocity within a…

The problem of a weak shock, reflected and diffracted by a wedge, is studied for the two-dimensional compressible Euler system. Some recent developments are overviewed and a perspective is presented within the context of a real gas, modeled…

When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge, governed by the Euler equations, there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle…