Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with nonlinear diffusion

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Zheng, Jiashan¹ 

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

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

DOI  :  10.1016/j.jde.2017.04.005

来源: Elsevier

【 摘 要 】

The coupled quasilinear Keller-Segel-Navier-Stokes system {n(t) + u center dot del n = triangle n(m) - del center dot (n del c), x is an element of Omega, t > 0, c(t) + u center dot del c = triangle c - c+n, x is an element of Omega,t > 0, u(t) + kappa(u center dot del)u + del P = triangle u + n del phi, x epsilon Omega, t > 0, del center dot u = 0, x is an element of Omega,t > 0 (KSNF) is considered under Neumann boundary conditions for n and c and no-slip boundary conditions for u in three-dimensional bounded domains Omega subset of R-3 with smooth boundary, where m > 0, K is an element of R are given constants, phi is an element of W-1,W-infinity(Omega). If m > 2, then for all reasonably regular initial data, a corresponding initial-boundary value problem for (KSNF) possesses a globally defined weak solution. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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