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CONVERGENCE RATES OF SOLUTIONS FOR A TWO-SPECIES CHEMOTAXIS-NAVIER-STOKES SYTSTEM WITH COMPETITIVE KINETICS
文献类型：期刊
通讯作者：Xiang, T (reprint author), Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China.
期刊名称：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B影响因子和分区
年：2019
卷：24
期：4
页码：1919-1942
ISSN：1531-3492
关键词：Chemotaxis-fluid system; boundedness; exponential convergence; algebraic convergence; convergence rates
所属部门：数学科学研究院
摘要：We study the convergence rates of solutions to the two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics: {(n(1))(t) + u .del n(1) = Delta n(1) - x(1)del . (n(1)del c) + mu(1)n(1)(1 - n(1) - a(1)n(2)), x is an element of Omega, t > 0, (n(2))(t) + u . del n(2) = Delta n(2) - x(2)del . (n(2)del c) + mu(2)n(2)(1 - a(2)n(1) - n(2)), x is an element of Omega , t > 0, c(t) + u . del c = Delta c - (alpha n(1) + beta n(2))c, x is an element of Omega, t > 0, u(t ...More
We study the convergence rates of solutions to the two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics: {(n(1))(t) + u .del n(1) = Delta n(1) - x(1)del . (n(1)del c) + mu(1)n(1)(1 - n(1) - a(1)n(2)), x is an element of Omega, t > 0, (n(2))(t) + u . del n(2) = Delta n(2) - x(2)del . (n(2)del c) + mu(2)n(2)(1 - a(2)n(1) - n(2)), x is an element of Omega , t > 0, c(t) + u . del c = Delta c - (alpha n(1) + beta n(2))c, x is an element of Omega, t > 0, u(t) + kappa(u . del)u = Delta u + del P + (gamma n(1) + delta n(2))del phi, del . u = 0, x is an element of Omega, t > 0 under homogeneous Neumann boundary conditions for n(1),n(2),c and no-slip boundary condition for u in a bounded domain Omega subset of R-d (d is an element of {2, 3}) with smooth boundary. The global existence, boundedness and stabilization of solutions have been obtained in 2-D [8] and 3-D for kappa = 0 and max{X1,X2}/min{mu 1,mu 2} parallel to c(0)parallel to(L infinity) (Omega) being sufficiently small [4]. Here, we examine further convergence and derive the explicit rates of convergence for any supposedly given global bounded classical solution (n(1),n(2),c,u); more specifically, in L-infinity-topology, we show that (n(1)(., t), n(2)(., t), u(., t)) ->(t ->infinity){ (1-a(1)/1-a(1)a(2),( )1-a(2)/1-a(1)a(2),0) exponentially, if a(1), a(2) is an element of (0, 1), (0,1,0) exponentially, if a(1) > 1 > a(2), (0, 1, 0) algebraically, if a(1) = 1 > a(2), (1, 0, 0) exponentially, if a(2) > 1 > a(1), (1, 0, 0) algebraically, if a(2) = 1 > a(1). In either cases, the c-solution component converges exponentially to 0. Moreover, it is shown that only the rate of convergence for u is expressed in terms of the model parameters and the first eigenvalue of -Delta in Omega under homogeneous Dirichlet boundary conditions, and all other rates of convergence are explicitly expressed only in terms of the model parameters alpha(i),mu(i), alpha and beta and the space dimension d. ...Hide

DOI：10.3934/dcdsb.2018249
百度学术：CONVERGENCE RATES OF SOLUTIONS FOR A TWO-SPECIES CHEMOTAXIS-NAVIER-STOKES SYTSTEM WITH COMPETITIVE KINETICS
语言：外文
被引频次：6
人气指数：1
浏览次数：1
基金：NSF of ChinaNational Natural Science Foundation of China [11501218, 11601516, 11571363]; Fundamental Research Funds for the Central UniversitiesFundamental Research Funds for the Central Universities [2017MS107]; Research Fund of Renmin University of China [2018030199]
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