Two dimensional subsonic and subsonic-sonic spiral flows outside a porous body

TL;DR

This paper studies the existence, uniqueness, and decay properties of two-dimensional subsonic and subsonic-sonic spiral flows outside a porous body using variational methods and elliptic estimates.

Contribution

It introduces a variational approach to establish existence and uniqueness of spiral flows and derives decay rates at infinity, including the subsonic-sonic limit solution.

Findings

Existence and uniqueness of subsonic spiral flows proven.

Decay rates at far fields are explicitly derived.

Subsonic-sonic limit solutions are obtained through approximation.

Abstract

In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation. The optimal decay rate at far fields is also derived by the Kelvin's transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compactness framework.