Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces

Abstract

<p style='text-indent:20px;'>The paper is concerned with the Navier-Stokes-Nernst-Planck-Poisson system arising from electrohydrodynamics in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^d $\end{document}</tex-math></inline-formula>. By means of the implicit function theorem, we prove the global existence of mild solutions for Cauchy problem of this system with small initial data in critical Besov-Morrey spaces. In comparison to the previous works, our existence result provides a new class of initial data, for which the problem is global solvability. Meanwhile, based on the so-called Gevrey estimates, we verify that the obtained mild solutions are analytic in the spatial variables. As a byproduct, we show the asymptotic stability of solutions as the time goes to infinity. Furthermore, decay estimates of higher-order derivatives of solutions are deduced in Morrey spaces.