Gevrey class regularity and stability for the Debye-Huckel system in critical Fourier-Besov-Morrey spaces

Achraf  Azanzal; Chakir Allalou; Said Melliani

doi:10.5269/bspm.62517

Achraf Azanzal Sultan Moulay Slimane University https://orcid.org/0000-0001-7449-2202
Chakir Allalou Sultan Moulay Slimane University https://orcid.org/0000-0002-4885-9397
Said Melliani Sultan Moulay Slimane University https://orcid.org/0000-0002-5150-1185

Abstract

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.

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References

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