Applications of a formula on Beltrami flow

TL;DR

This paper introduces a new formula involving divergence and curl operators to establish uniqueness results for Beltrami flows and applies it to Maxwell and Stokes eigenvalue problems.

Contribution

It presents a novel elementary formula involving divergence and curl operators, enabling new uniqueness results for Beltrami flows and applications to eigenvalue problems.

Findings

Proved uniqueness of Beltrami flows in bounded and unbounded domains.

Applied the formula to Maxwell and Stokes eigenvalue problems.

Provided a new analytical tool for fluid dynamics and electromagnetism.

Abstract

In this note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators $\divg$ and $\curl$. We also use this formula to deal with Maxwell and Stokes eigenvalue problems.