Uniqueness of the stochastic Keller–Segel model in one dimension

Abstract

In a recent paper (J. Differential Equations, 310: 506–554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak–Keller–Segel system in 1 dimension (1D), driven by time-homogeneous spatial Wiener processes. The current paper is a continuation and consists of two results about the stochastic Patlak–Keller–Segel system. First, we establish some additional regularity results of the solutions. The additional regularity is, e.g. important for its numerical modelling. Then, as a second result, we obtain the pathwise uniqueness of the solutions to the stochastic Patlak–Keller–Segel system. Finally, we conclude the paper with the existence of strong solution to this system in 1D. © 2026 Elsevier B.V.