Gevrey Class Regularity and Stability for the Debye-Hu spacing diaeresis ckel System in Critical Fourier-Besov-Morrey Spaces

In this paper, we study the analyticity of mild solutions to the Debye-Hu center dot ckel system with small initial data in critical Fourier-Besov-Morrey spaces. Specifically, by using the Fourier localization argument, the Littlewood-Paley theory and bilinear-type fixed point theory, we prove that global-in-time mild solutions are Gevrey regular. As a consequence of analyticity, we get time decay of mild solutions in Fourier-Besov-Morrey spaces. Finally, we show a blow-up criterion of the local-in-time mild solutions of the Debye-Hu center dot ckel system.