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arXiv · 1711.06603

Well-posedness of a Debye type system endowed with a full wave equation

Arnaud Heibig
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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.

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Arnaud Heibig. 2017-11-17. Well-posedness of a Debye type system endowed with a full wave equation. https://arxiv.org/abs/1711.06603

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