A simple proof of concentration of mass equal to for blowing up N -symmetric solutions of the Keller–Segel model of chemotaxis in two dimensions with large N is given. Moreover, a criterion for blowup of solutions in terms of the radial initial concentrations, related to suitable Morrey spaces norms, is derived for radial solutions of chemotaxis in several dimensions. This condition is, in a sense, complementary to the one guaranteeing the global-in-time existence of solutions. The integrals with no integration limits are understood as over the whole space : . The letter C denotes various constants which may vary from line to line but they are independent of solutions. As usual, denotes the area of the unit sphere in .
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Biler et al. (2015) studied this question.