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 → ∞.
Highlights
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
The purpose of this paper is to prove the well-posedness and Gevrey analyticity of Equation (1) in the Besov spaces
Summary
We consider existence and regularity of mild solutions for the initial value problem of the following fractional porous medium equation (FPME) in n for n ≥ 2 :. Biler and Wu [4] studied global well-posedness of the equation with ( ) small initial data in the critical Besov spaces B 21,−qα 2 for 1 < α < 2. We refer it by PME, and the classical properties of this equation can be found in literature [6] It can describe the movement of an ideal gas flowing through a porous medium or be regarded as a kind of non-local quadratic evolution problem. We will consider well-posedness and Gevrey analyticity of the fractional porous medium Equation (1) with initial data in critical Besov spaces.
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