On the ill posedness of Force-Free Electrodynamics in Euler Potentials
Abstract
We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed. We establish this result by showing that a well-posedness criterion provided by Kreiss fails to hold for this theory, and using a theorem provided by Strang. To show the nature of the problem we display a particular bounded (in Sobolev norms) sequence of initial data for the Force-free equations such that at any given time as close to zero as one wishes, the corresponding evolution sequence is not bounded. Thus, the Force-free evolution is non continuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
Cite
@article{arxiv.1611.06415,
title = {On the ill posedness of Force-Free Electrodynamics in Euler Potentials},
author = {Oscar A. Reula and Marcelo E. Rubio},
journal= {arXiv preprint arXiv:1611.06415},
year = {2017}
}
Comments
13 pages, no figures, accepted for publication in Phys. Rev. D