The inviscid limit and well-posedness for the Euler–Nernst–Planck–Poisson system

ABSTRACT

In this paper, we mainly study the Cauchy problem of the Euler–Nernst–Planck–Poisson (ENPP) system. We first establish local well-posedness for the Cauchy problem of the ENPP system in Besov spaces. Then we present a blow-up criterion of solutions to the ENPP system. Moreover, we prove that the solutions of the Navier–Stokes–Nernst–Planck–Poisson system converge to the solutions of the ENPP system as the viscosity ν goes to zero, and the convergence rate is at least of order ${\nu }^{1/2}$.

KEYWORDS:

• The Euler–Nernst– Planck–Poisson system
• the Navier–Stokes–Nernst–Planck–Poisson system
• local well-posedness
• blow-up
• the inviscid limit

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35Q30
• 35M10
• 76N10
• 35B44
• 41A25

Acknowledgements

The authors thank the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Zhang is supported by National Nature Science Foundation of China [grant number 11626177] and by the Fundamental Research Funds for the Central Universities [WUT: 2016IVA080]. Yin was partially supported by NNSFC [number 11671407], FDCT [number 098/2013/A3], Guangdong Special Support Program [number 8-2015], and the key project of NSF of Guangdong Province [number 2016A030311004].