Gevrey class regularity of solutions to the Nernst–Planck–Poisson equations with generalized dissipation

Abstract

In this article, we consider Nernst–Planck–Poisson system with generalized dissipation. First, we prove the Gevrey class regularity of local solutions to system with large rough initial data in modulation spaces . Secondly, applying so-called Gevrey estimates, which is motivated by the works of Foias and Temam, we establish Gevrey class regularity of solutions to the system with initial data in a certein critical Fourier–Besov spaces . The results of us particularly imply that the solution is analytic in the spatial variable and obtain temporal decay rates of higher Fourier–Besov norms of solutions.

Keywords:

• Nernst–Planck–Poisson equations
• Modulation spaces
• Fourier–Besov spaces
• Gevrey regularity

AMS Subject Classifications:

• Primary: 35Q35
• Secondary: 35B40
• 35B65
• 76A15

Acknowledgements

The author would like to thank Professor Lixin Yan for helpful discussions.

Notes

No potential conflict of interest was reported by the authors.