Blow-up prevention by nonlinear diffusion in a 2D Keller-Segel-Navier-Stokes system with rotational flux

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Zheng, Jiashan¹  Ke, Yuanyuan² 

[1] Ludong Univ, Sch Math & Stat Sci, Yantai 264025, Peoples R China

[2] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

关键词: Navier-Stokes system;    Keller-Segel model;    Global existence;    Nonlinear diffusion;   

DOI  :  10.1016/j.jde.2019.11.071

来源: Elsevier

【 摘 要 】

This paper deals with a boundary-value problem for a coupled chemotaxis-Navier-Stokes system involving tensor-valued sensitivity with saturation {n(t) + u . del n = Delta n(m) - del . (nS(x, n, c)del c), x is an element of Omega, t > 0, (KSNS) c(t) + u . del c = Delta c + n, x is an element of Omega, t > 0, u(t) + k(u . del)u + del P = Delta u + n del phi, x is an element of Omega, t > 0, del . u = 0, x is an element of Omega, t > 0, which describes chemotaxis-fluid interaction in cases when the evolution of the chemoattractant is essentially dominated by production through cells, where k is an element of R, phi is an element of W-2,W-infinity(Omega) and S is a given function with values in R-2x2 which fulfills vertical bar S(x, n, c)vertical bar <= C-S with some C-S > 0. If m > 1 and Omega subset of R-2 is a bounded domain with smooth boundary, then for all reason-ably regular initial data, a corresponding initial-boundary value problem for (KSNS) possesses a global (weak) solution which is bounded. Our main tool is consideration of the energy functional integral(Omega)n(m) + integral(Omega)vertical bar del c vertical bar(2). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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