Well-posedness for the Euler-Nernst-Planck-Possion system in Besov spaces

TL;DR

This paper establishes local well-posedness, blow-up criteria, and convergence results for the Euler-Nernst-Planck-Possion system in Besov spaces, advancing understanding of its mathematical properties and relation to Navier-Stokes solutions.

Contribution

It introduces the first local well-posedness results for the ENPP system in Besov spaces and analyzes the convergence of Navier-Stokes-Nernst-Planck-Possion solutions as viscosity vanishes.

Findings

Local well-posedness in Besov spaces

Blow-up criterion for solutions

Convergence of Navier-Stokes-Nernst-Planck-Possion to ENPP as viscosity tends to zero

Abstract

In this paper, we mainly study the Cauchy problem of the Euler-Nernst-Planck-Possion ($ENPP$) 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-Possion system converge to the solutions of the $ENPP$ system as the viscosity $\nu$ goes to zero, and that the convergence rate is at least of order ${\nu}^\frac{1}{2}$.