Gevrey class regularity and stability for the Debye-Huckel system in critical Fourier-Besov-Morrey spaces - Achraf Azanzal; Chakir Allalou; Said Melliani (Boletim da Sociedade Paranaense de Matemática, 2022)
In this paper, we study the analyticity of mild solutions to the Debye-Huckel 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-BesovMorrey spaces. Finally, we show a blow-up criterion of the local-in-time mild solutions of the Debye-Huckel system.