Well-posedness of a Debye type system endowed with a full wave equation
Analysis of PDEs
2018-01-26 v3
Abstract
We prove well-posedness for a transport-diffusion problem coupled with a wave equation for the potential. We assume that the initial data are small. A bilinear form in the spirit of Kato's proof for the Navier-Stokes equations is used, coupled with suitable estimates in Chemin-Lerner spaces. In the one dimensional case, we get well-posedness for arbitrarily large initial data by using Gagliardo-Nirenberg inequalities.
Keywords
Cite
@article{arxiv.1711.06603,
title = {Well-posedness of a Debye type system endowed with a full wave equation},
author = {Arnaud Heibig},
journal= {arXiv preprint arXiv:1711.06603},
year = {2018}
}