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Indexed by:期刊论文

Date of Publication:2018-05-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE

Volume:461

Issue:2

Page Number:1748-1770

ISSN No.:0022-247X

Key Words:Chemotaxis; Keller-Segel system; Navier-Stokes equation; Global solutions; Decay estimates

Abstract:In this paper, we consider the following Keller-Segel-Navier-Stokes system
   {n(t) = Delta n - del. (nS(x,n,c) . del c) - u . del n in Omega x (0, T),
   c(t) = Delta c - c + n . del c in Omega x (0, T),
   u(t) = Delta u - (u . del)u + del P + n del Phi, del . u = 0 in Omega x (0, T),
   subject to the boundary condition del c.v = (del n - nS(x,n, c) . del c).nu = 0, u = 0, and the initial data (n(0)(x), c(0)(x), u(0)(x)), where Omega subset of R-N is a smooth bounded domain with N is an element of {2, 3}, nu denotes the unit outer normal of partial derivative Omega, S is an element of C-2((Omega) over barx [0, infinity)(2))(NxN) and Phi is an element of C1+delta((Omega) over bar) with delta is an element of (0,1). We establish global' classical solutions decaying to the constant steady state ((n) over bar (0), (n) over bar (0), 0) exponentially with (n) over bar (0) := 1/vertical bar Omega vertical bar integral(Omega) n0(x)dx, whenever parallel to n(0)parallel to (L N/2 (Omega)), parallel to del c(0)parallel to)(LN (Omega)) and parallel to u(0)parallel to (LN (Omega)) small enough. (C) 2017 Elsevier Inc. All rights reserved.