A Keller-Segel-fluid system with singular sensitivity: Generalized solutions

被引：8

作者：

Black, Tobias ^{[1
]}

Lankeit, Johannes ^{[1
]}

Mizukami, Masaaki ^{[2
]}

机构：

[1] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany

[2] Tokyo Univ Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2019年 / 42卷 / 09期

基金：

日本学术振兴会;

关键词：

chemotaxis-fluid; global existence; Keller-Segel system; singular sensitivity; Stokes equation; PARABOLIC CHEMOTAXIS SYSTEM; STOKES SYSTEM; BOUNDEDNESS;

D O I：

10.1002/mma.5561

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In bounded smooth domains omega subset of RN, N is an element of {2,3}, we consider the Keller-Segel-Stokes systemnt+u center dot backward difference n=Delta n-chi backward difference center dot backward difference c,ct+u center dot backward difference c=Delta c-c+n,ut=Delta u+ backward difference P+n backward difference phi, backward difference center dot u=0, and prove global existence of generalized solutions if chi<infinity,N=2,53,N=3. These solutions are such that blow-up into a persistent Dirac-type singularity is excluded.

引用

页码：3002 / 3020

页数：19

共 19 条

[1] Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues [J].