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Inviscid limit for the hyperbolic Keller--Segel equations in B∞,11

  • Yang Cen
  • Zhaoyang Yin
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Abstract

In this paper, we study the inviscid limit for the hyperbolic Keller--Segel equations with logistic sensitivity 1−u. We establish a common existence time and a priori estimates uniform with respect to the diffusion coefficient in the critical Besov spaces Bp,11+d/p(Rd) with 1≤ p≤∞. For 1<p<∞, we obtain explicit convergence rates in Bp,10, and we also give estimates for the case p=1. For initial data in B∞,11, we prove convergence at rate O(ε1/2) in L∞, a bound of order O(ε1/2log(e/ε)) in B∞,10, and strong convergence in L∞(0,T;B∞,11). Additional regularity of the initial data yields improved convergence rates. We construct a fixed initial datum showing that the exponent 1/2 in L∞ is optimal.

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Cite

BibTeXRIS
BibTeX
@misc{cen2026inviscid,
  title = {{Inviscid limit for the hyperbolic Keller--Segel equations in $B_\infty,1^1$}},
  author = {Yang Cen and Zhaoyang Yin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41670},
  eprint = {2610.41670},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41670},
}
RIS
TY  - UNPB
TI  - Inviscid limit for the hyperbolic Keller--Segel equations in B_∞,1^1
AU  - Yang Cen
AU  - Zhaoyang Yin
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41670
UR  - https://arxiv.org/abs/2610.41670
AB  - In this paper, we study the inviscid limit for the hyperbolic Keller--Segel equations with logistic sensitivity 1−u. We establish a common existence time and a priori estimates uniform with respect to the diffusion coefficient in the critical Besov spaces B_p,1^1+d/p(R^d) with 1≤ p≤∞. For 1<p<∞, we obtain explicit convergence rates in B_p,1^0, and we also give estimates for the case p=1. For initial data in B_∞,1^1, we prove convergence at rate O(ε^1/2) in L^∞, a bound of order O(ε^1/2log(e/ε)) in B_∞,1^0, and strong convergence in L^∞(0,T;B_∞,1^1). Additional regularity of the initial data yields improved convergence rates. We construct a fixed initial datum showing that the exponent 1/2 in L^∞ is optimal.
ER  -