Global well-posedness for Euler-Nernst-Planck-Possion system in dimension two

TL;DR

This paper proves the global well-posedness of the Euler-Nernst-Planck-Poisson system in two dimensions for a broad class of initial data within certain Sobolev spaces, advancing understanding of this coupled PDE system.

Contribution

It establishes the first global well-posedness results for the Euler-Nernst-Planck-Poisson system in two dimensions with general initial data in specific Sobolev spaces.

Findings

Global well-posedness in 2D for initial data in specified Sobolev spaces.

Conditions on Sobolev indices ensuring existence and uniqueness.

Extension of well-posedness theory to coupled electrohydrodynamic systems.

Abstract

In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion system. We obtain global well-posedness for the system in dimension $d=2$ for any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)$ under certain conditions of $s_1$ and $s_2$.