On the Construction of Beltrami Fields and Associated Boundary Value Problems

Abstract

In this paper, we present two simple methods for constructing Beltrami fields. The first one consists of a composition of operators, including a quaternionic transmutation operator as well as the computation of formal powers for the function \(f(x)=e^{\textbf{i}\lambda x}\). For the second method, we generate Beltrami fields from harmonic functions, and using the intrinsic relation between the normal and tangential derivative, we solve an associated Neumann-type boundary value problem.