Global well posedness for a 2D drift–diffusion–Maxwell system

Abstract

We prove global existence of regular solutions to the drift–diffusion–Maxwell system in two space dimension. We also provide an exponential growth estimate for the norm of the solution when the time goes to infinity.

Keywords:

• Maxwell system
• drift–diffusion model
• global well posedness

AMS Subject Classifications:

• 35Q61
• 76R50

Acknowledgements

We are very grateful to Professor Nader Masmoudi for interesting discussions around the questions dealt with in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.