TY - JOUR

T1 - Singular limit problem for the Keller–Segel system and drift–diffusion system in scaling critical spaces

AU - Kurokiba, Masaki

AU - Ogawa, Takayoshi

N1 - Funding Information:
The authors would like to thank Professor Kenji Yajima for his pointing out a mistake in the original paper. The work of T. Ogawa is partially supported by JSPS Grant in aid for Scientific Research S #25270702, A #19H00638 and Challenging Research (Pioneering) #17H06199. The work of M. Kurokiba is partially supported by JSPS Grant in aid for Scientific Research C #16K05219.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We consider a singular limit problem for the Cauchy problem of the Keller–Segel equation in a critical function space. We show that a solution to the Keller–Segel system in a scaling critical function space converges to a solution to the drift–diffusion system of parabolic–elliptic type (the simplified Keller–Segel model) in the critical space strongly as the relaxation time τ→ ∞. For the proof of singular limit problem, we employ generalized maximal regularity for the heat equation and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(Rn) and F˙q,σs(Rn).

AB - We consider a singular limit problem for the Cauchy problem of the Keller–Segel equation in a critical function space. We show that a solution to the Keller–Segel system in a scaling critical function space converges to a solution to the drift–diffusion system of parabolic–elliptic type (the simplified Keller–Segel model) in the critical space strongly as the relaxation time τ→ ∞. For the proof of singular limit problem, we employ generalized maximal regularity for the heat equation and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(Rn) and F˙q,σs(Rn).

KW - Critical space

KW - Drift–diffusion system

KW - Global well-posedness

KW - Keller–Segel equation

KW - Maximal regularity

KW - Scaling invariance

KW - Singular limit problem

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U2 - 10.1007/s00028-019-00527-3

DO - 10.1007/s00028-019-00527-3

M3 - Article

AN - SCOPUS:85071184044

VL - 20

SP - 421

EP - 457

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 2

ER -