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In a recent paper (J. Differential Equations, 310: 506-554, 2022), theauthors proved the existence of martingale solutions to a stochastic version ofthe classical Patlak-Keller-Segel system in 1 dimension (1D), driven bytime-homogeneous spatial Wiener processes. The current paper is a continuationand consists of two results about the stochastic Patlak-Keller-Segel system in1D. First, we establish some additional regularity results of the solutions.The additional regularity is, e.g. important for its numerical modeling. Then,as a second result, we obtain the pathwise uniqueness of the solutions to thestochastic Patlak-Keller-Segel system in 1D. Finally, we conclude the paperwith the existence of the strong solution to this system in 1D.

Uniqueness of the stochastic Keller-Segel model in one dimension