Unboundedness for solutions to a degenerate drift-diffusion equation with the \(L^{1}\)-supercritical and the energy subcritical exponent
The author studies the large time behavior of weak solutions to a degenerate drift-diffusion system related to Smoluchowski-Poisson and Keller-Segel models \[ u_t=\Delta(u^\alpha)-\nabla\cdot(\rho\nabla\psi), \] \[ -\Delta\psi=\rho. \] For \(\alpha\in[\frac{2n}{n+2},2-\frac2n]\), i.e. in the range of \(\alpha\) between the energy and the \(L^1\) critical cases, this asymptotics is classified by the invariant norms of initial data and initial values of energy/entropy functional.
scientific article; zbMATH DE number 6852179
scientific article