The goal of this talk is to prove the existence for the Keller-Segel equation with the initial data in Besov-Morrey spaces. A closer inspection shows that the maximal regularity has a lot to do with the local means in the theory of function spaces. It is well known that the second integrability index of Besov spaces plays an important role to compare the property of functions. This fact will be included in our theorem in maximal regularity. This is a joint work with Toru Nogayama at Chuo University.

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