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

Ogawa, Takayoshi Suguro, Takeshi 京都大学 DOI:10.1007/s00208-022-02469-7

2023.10

概要

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

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