Uniform L^∞ boundedness for a degenerate parabolic-parabolic Keller-Segel model

This paper investigates the existence of a uniform in time L∞ bounded weak entropy solution for the quasilinear parabolic-parabolic KellerSegel model with the supercritical diffusion exponent 0 < m < 2 - 2/d in the multi-dimensional space ℝd under the condition that the L d(2-m)/2 norm of initial data is smaller than a universal constant. Moreover, the weak entropy solution u(x,t) satisfies mass conservation when m > 1-2/d. We also prove the local existence of weak entropy solutions and a blow-up criterion for general L1 ∩ L∞ initial data.

Duke Scholars

Author Jian-Guo Liu Physics