Microscopic derivation of the Keller-Segel equation in the sub-critical regime

We derive the two-dimensional Keller-Segel equation from a stochastic system of $N$ interacting particles in the case of sub-critical chemosensitivity $\chi < 8 \pi$. The Coulomb interaction force is regularised with a cutoff of size $N^{- \alpha}$, with arbitrary $\alpha \in (0, 1 / 2)$. In particular we obtain a quantitative result for the maximal distance between the real and mean-field $N$-particle trajectories.

• Publication year

  2017

• Venue

  arXiv: Analysis of PDEs

• Publication date

  2017-03-13

• Fields of study

  Mathematics, Physics

• Identifiers
  arXiv 1703.04376
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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