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 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.
Keywords
Cite
@article{arxiv.2209.13188,
title = {Uniqueness of the stochastic Keller-Segel model in one dimension},
author = {Erika Hausenblas and Debopriya Mukherjee and Thanh Tran},
journal= {arXiv preprint arXiv:2209.13188},
year = {2022}
}
Comments
21 pages