Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ<sup>2</sup>
Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ<sup>2</sup>
Abstract We analyze the two‐dimensional parabolic‐elliptic Patlak‐Keller‐Segel model in the whole Euclidean space ℝ 2 . Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local‐in‐time existence for any mass of “free‐energy solutions,” namely weak solutions with some free‐energy estimates. We also prove …