arXiv subjects

Minghong Han

Publications and source records attributed to Minghong Han.

2 recordsLinked to original sources

arXiv2026

Supersonic flow of a Chaplygin gas past a conical wing with $\Lambda$-shaped cross sections

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 steady isentropic irrotational compressible Euler equations. This work is motivated by the design of the Nonweiler wing, which is one of the simplest waveriders. Mathematically, the problem reduces to a boundary value problem for a nonlinear mixed-type equation in conical coordinates. By introducing a viscosity parameter to treat the degenerate boundary, we use the continuity method to establish the existence of a piecewise smooth self-similar solution to the problem, in the case that the shock is attached to the leading edge of the conical wing. Our results verify part of K\"uchemann's speculation on the conical flow field structures of this type, and also find a new conical flow field structure.

math.AP↗

arXiv2025

Uniqueness of transonic shock solutions in general approximate nozzles for steady potential flow

We study the uniqueness of solutions with a transonic shock in a two-dimensional Riemannian manifold with a special metric, which can be regarded as an approximate model of the general physical nozzles, within a class of transonic shock solutions for steady potential flow. We first prove the uniqueness of these solutions on the unit 2-sphere: for given uniform supersonic upstream flow at the entry, there exists a unique uniform pressure at the exit such that a transonic shock solution exists in the sphere, which is unique modulo a translation. A similar result is then extended to a class of manifolds. Mathematically, it is equivalent to showing a uniqueness theorem for a free boundary problem of a second-order elliptic-hyperbolic mixed-type partial differential equation in the general approximate nozzles. The proof is based on the maximum/comparison principle with a suitable special transonic shock solution as a comparison function.

math.AP↗