The Keller-Segel system of parabolic-parabolic type with initial data in weak Ln/2(ℝn) and its application to self-similar solutions

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Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension (2010, background): “Therefore, we are not able to obtain here a local existence result without any smallness conditions, nor to improve the known smallness condition for the global existence when ε > 0 (see [21, 40] for the global existence under smallness conditions and [36, 51] for the existence vs.”
Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces (2009, background): “Hence it seems to be an interesting question whether we can construct a global solution of (KS) with u0 ∈ L 2 (Rn) and v0 ∈ BMO, which was discussed in [17] by the authors.”
Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller--Segel equations in the whole space (2013, unknown): “Thus, Proposition 3 is proved.”