Boundedness in a three-dimensional chemotaxis-fluid system involving tensor-valued sensitivity with saturation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:442

Article

Zheng, Jiashan¹ 

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

关键词: Boundedness;    Chemotaxis-fluid system;    Global existence;    Tensor-valued sensitivity;   

DOI  :  10.1016/j.jmaa.2016.04.047

来源: Elsevier

【 摘 要 】

We consider the chemotaxis-fluid system {n(t) + u center dot del n = del center dot (D(n)del n) - del center dot (nS(x, n, c) center dot del c) + an - bn(2), x is an element of Omega, t > 0, c(t) + u center dot del c - del c - c + n, x is an element of Omega, t > 0, (CF) u(t) + del P = del u + n del phi + g(x,t), x is an element of Omega, t > 0, del center dot u = 0, x is an element of Omega, t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain Omega subset of R-3, where phi is an element of W-1,W-infinity(Omega), a >= 0 and b > 0. Here g is an element of C-1((Omega) over bar x [0, infinity)) boolean AND L-infinity (Omega x (0, infinity)), D(n) >= u(m-1), vertical bar S(x,n,c)vertical bar <= (1 + n)(-alpha), and the parameter alpha > 0. If m > max{6/5 - alpha, 1/3}, then for all reasonably regular initial data, a corresponding initial-boundary value problem for (CF) possesses a globally defined weak solution through the Moser-type iteration. (C) 2016 Elsevier Inc. All rights reserved.

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