Axisymmetric flow of ideal fluid moving in a narrow domain: a study of the axisymmetric hydrostatic Euler equations

TL;DR

This paper introduces a new mathematical model for axisymmetric ideal fluid flow in narrow domains, proves its well-posedness, justifies its derivation rigorously, and discusses conditions leading to blowup scenarios.

Contribution

The paper presents a novel model for axisymmetric fluid flow in narrow domains, with rigorous mathematical validation and analysis of blowup behavior.

Findings

Model accurately describes leading order behavior of the flow.

Well-posedness established under a new sign condition.

Blowup phenomena are analyzed and discussed.

Abstract

In this article we will introduce a new model to describe the leading order behavior of an ideal and axisymmetric fluid moving in a very narrow domain. After providing a formal derivation of the model, we will prove the well-posedness and provide a rigorous mathematical justification for the formal derivation under a new sign condition. Finally, a blowup result regarding this model will be discussed as well.