TITLE:
Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces
AUTHORS:
Weiliang Xiao, Yu Zhang
KEYWORDS:
Well-Posedness, Gevrey Regularity, Time Decay, Besov Spaces
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.1,
January
19,
2022
ABSTRACT: In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p q ≤ ∞, and analyticity of solutions with 1 p q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.