# Nonexistence of compressible irrotational inviscid flows along infinite protruding corners

## TL;DR

This paper proves that irrotational, subsonic inviscid flows cannot have a nonzero velocity limit at infinity along infinite protruding corners, highlighting the generation of vorticity in rotational flows.

## Contribution

It establishes the nonexistence of irrotational solutions with specified boundary conditions in certain geometric configurations, revealing vorticity generation mechanisms.

## Key findings

- Irrotational subsonic flows do not exist along infinite protruding corners.
- Rotational flows can exist under the same conditions.
- Vorticity can be generated by slip-condition boundaries in inviscid flows.

## Abstract

We consider inviscid flow with isentropic coefficient greater than one. For flow along smooth infinite protruding corners we attempt to impose a nonzero limit for velocity at infinity at the upstream wall. We prove that the problem does not have any irrotational uniformly subsonic solutions, whereas rotational flows do exist. This can be considered a case of a slip-condition solid "generating" vorticity in inviscid flow.