Supercritical degenerate parabolic–parabolic Keller–Segel system: existence criterion given by the best constant in Sobolev’s inequality

• DOI: 10.1007/s00033-019-1115-1
• Publication Date: 2019-04-10T12:13:25Z
• Authors: Jinhuan Wang; Yue Li; Li Chen
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; Analysis of PDEs (math.AP)

This article presents a relationship between the sharp constant of the Sobolev inequality and the initial criterion to the global existence of degenerate parabolic-parabolic Keller-Segel system with the diffusion exponent $\frac{2n}{2+n}