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PreprintCC BY 4.0arXiv

Well-posedness of 2D stochastic parabolic-parabolic Keller-Segel system with logistic source

  • Erika Hausenblas
  • Boris Jidjou Moghomye
  • Paul Andre Razafimandimby
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Abstract

We consider a stochastic, fully parabolic Keller-Segel system with multiplicative noise in non-divergence form and a logistic source in a two-dimensional bounded domain, subject to random initial data. We construct a global-in-time, non-negative martingale solution by means of a suitable regularisation procedure, combined with Banach fixed-point arguments, a localisation procedure, and a stochastic compactness method. We further establish pathwise uniqueness and uniqueness in law for martingale solutions, and prove the existence of a unique global-in-time, non-negative weak solution without imposing any smallness condition on the initial data.

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Cite

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BibTeX
@misc{hausenblas2026wellposedness,
  title = {{Well-posedness of 2D stochastic parabolic-parabolic Keller-Segel system with logistic source}},
  author = {Erika Hausenblas and Boris Jidjou Moghomye and Paul Andre Razafimandimby},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22458},
  eprint = {2610.22458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22458},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Well-posedness of 2D stochastic parabolic-parabolic Keller-Segel system with logistic source
AU  - Erika Hausenblas
AU  - Boris Jidjou Moghomye
AU  - Paul Andre Razafimandimby
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22458
UR  - https://arxiv.org/abs/2610.22458
AB  - We consider a stochastic, fully parabolic Keller-Segel system with multiplicative noise in non-divergence form and a logistic source in a two-dimensional bounded domain, subject to random initial data. We construct a global-in-time, non-negative martingale solution by means of a suitable regularisation procedure, combined with Banach fixed-point arguments, a localisation procedure, and a stochastic compactness method. We further establish pathwise uniqueness and uniqueness in law for martingale solutions, and prove the existence of a unique global-in-time, non-negative weak solution without imposing any smallness condition on the initial data.
ER  -