TY - JOUR

T1 - Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space

AU - Kurokiba, Masaki

AU - Ogawa, Takayoshi

N1 - Funding Information:
The work of T. Ogawa is partially supported by JSPS Grant in aid for Scientific Research S # 19H05597 and Challenging Research (Pioneering) # 20K20284 . The work of M. Kurokiba is partially supported by JSPS Grant in aid for Scientific Research C # 19K03555 .
Publisher Copyright:
© 2020 Elsevier Inc.

PY - 2020/11/5

Y1 - 2020/11/5

N2 - We consider the singular limit problem of the Cauchy problem to the Keller-Segel equation in the two dimensional critical space. It is shown that the solution to the Keller-Segel system in the scaling critical function space converges to the solution to the drift-diffusion system of parabolic-elliptic equations (the simplified Keller-Segel equation) in the critical space strongly as the relaxation time parameter τ→∞. For the proof, we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(R2) and F˙q,σs(R2) for the proof of singular limit problem.

AB - We consider the singular limit problem of the Cauchy problem to the Keller-Segel equation in the two dimensional critical space. It is shown that the solution to the Keller-Segel system in the scaling critical function space converges to the solution to the drift-diffusion system of parabolic-elliptic equations (the simplified Keller-Segel equation) in the critical space strongly as the relaxation time parameter τ→∞. For the proof, we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(R2) and F˙q,σs(R2) for the proof of singular limit problem.

KW - Bounded mean oscillation

KW - Critical space

KW - Drift-diffusion system

KW - Keller-Segel equation

KW - Maximal regularity

KW - Singular limit problem

UR - http://www.scopus.com/inward/record.url?scp=85086511761&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086511761&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2020.06.012

DO - 10.1016/j.jde.2020.06.012

M3 - Letter

AN - SCOPUS:85086511761

VL - 269

SP - 8959

EP - 8997

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 10

ER -