Author(s)

Weiliang Xiao, Yu Zhang^*

School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China.

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 < ∞, 1 ≤ q ≤ ∞, and analyticity of solutions with 1 < p < ∞, 1 ≤ 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 → ∞.

Well-Posedness, Gevrey Regularity, Time Decay, Besov Spaces

Xiao, W. and Zhang, Y. (2022) Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces. Journal of Applied Mathematics and Physics, 10, 91-111. doi: 10.4236/jamp.2022.101008.