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Uniqueness of the stochastic Keller-Segel model in one dimension

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arxiv 2209.13188 v1 pith:YU3MFQKD submitted 2022-09-27 math.AP math.PR

Erika Hausenblas , Debopriya Mukherjee , Thanh Tran This is my paper · ORCID
classification math.APmath.PR
keywords stochasticsystempatlak-keller-segelsolutionsadditionaldimensionexistenceregularity
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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 in 1D. 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 the stochastic Patlak-Keller-Segel system in 1D. Finally, we conclude the paper with the existence of the strong solution to this system in 1D.

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  1. The stochastic Keller--Segel system in critical spaces

    math.PR 2026-07 conditional novelty 6.0 of 10

    A stochastically forced Keller–Segel system in dimensions d≥3 admits maximal local solutions in scaling-critical Besov spaces, and small data guarantees arbitrarily long existence with high probability.

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