Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller–Segel system

Abstract We consider the singular limit problem for Cauchy of (Patlak–) Keller–Segel system parabolic-parabolic type. The is considered in uniformly local Lebesgue spaces and as relaxation parameter $$\tau $$ τ goes to infinity, solution equation converges a drift-diffusion strong topology. For proof, we follow former result due Kurokiba–Ogawa [20–22] establish maximal regularity heat over Morrey which are non-UMD Banach apply it convergence scaling critical spaces.