Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces

查看全文 作　　者：YANG [1]MingHua;FU [2]ZunWei;SUN [3]JinYi

机构地区：[1]School of Information Technology, Jiangxi University of Finance and Economics;[2]Department of Mathematics, Linyi University;[3]College of Mathematics and Statistics, Northwest Normal University

出　　处：《Science China Mathematics》索引2017年第60卷第10期,共20页

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11671185, 11301248 and 11271175) 摘　　要：We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the solution, when the initial data(u0, v0, w0) belongs to homogeneous Besov spaces˙B^(-2+3/p)_(p,1)(R^3) ×˙B^(-2+3/r)_(r,1)(R^3) ×˙B^(3/q)_(q,1)(R^3) for p, q and r satisfying some technical assumptions. Furthermore, we prove that if the initial data is sufficiently small, then the solution is global. Meanwhile, based on the so-called Gevrey estimates, we particularly prove that the solution is analytic in the spatial variable. In addition, we analyze the long time behavior of the solution and obtain some decay estimates for higher derivatives in Besov and Lebesgue spaces. 关键词：BESOV空间齐次趋化正则性系统衰减估计长时间行为柯西问题

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Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces

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