Green's functions of the induction equation on regions with boundary. I. General properties and a construction principle

Publisher Website
Google Scholar
Abstract
The evolution of a magnetic field is considered which pervades an electrically conducting fluid and its non‐conducting surroundings under the influence of electromotive forces due to internal motion and other causes. The governing equations ‐‐ among which the induction equation of magnetohydrodynamics is the most prominent ‐‐ pose an initial value problem for the magnetic flux density. Properties of this initial value problem and of the solving Green's function are reviewed and a general construction principle for the Green's function is given.Detailed treatment of cases where the fluid occupies a sphere or an evenly bounded half‐space are presented in two subsequent papers