Uniqueness of the stochastic Keller-Segel model in one dimension

2022/09/27 by Erika Hausenblas, Hausenblas, Erika, Debopriya Mukherjee +3 · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #Gene Regulatory Network Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2209.13188

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 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.

Cited by

• The stochastic Keller--Segel system in critical spaces

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