TY - JOUR

T1 - A Keller‐Segel‐fluid system with singular sensitivity

T2 - Generalized solutions

AU - Black, Tobias

AU - Lankeit, Johannes

AU - Mizukami, Masaaki

N1 - Funding Information: TB and JL acknowledge support of the Deutsche Forschungsgemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks (project no. 288366228). MM is funded by JSPS Research Fellowships for Young Scientists (No. 17J00101). A major part of this work was written during joint stays at Universität Paderborn and Tokyo University of Science under support from Tokyo University of Science.

PY - 2019/5/6

Y1 - 2019/5/6

N2 - In bounded smooth domains Ω ⊂ R N, N ∈ {2,3}, we consider the Keller-Segel-Stokes system (Formula presented.) and prove global existence of generalized solutions if (Formula presented.) These solutions are such that blow-up into a persistent Dirac-type singularity is excluded.

AB - In bounded smooth domains Ω ⊂ R N, N ∈ {2,3}, we consider the Keller-Segel-Stokes system (Formula presented.) and prove global existence of generalized solutions if (Formula presented.) These solutions are such that blow-up into a persistent Dirac-type singularity is excluded.

KW - Keller-Segel system

KW - Stokes equation

KW - chemotaxis-fluid

KW - global existence

KW - singular sensitivity

UR - http://www.scopus.com/inward/record.url?scp=85065245326&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1805.09085

DO - 10.48550/arXiv.1805.09085

M3 - Article

VL - 42

SP - 3002

EP - 3020

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 9

ER -