Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ 2

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 so... View More