Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces
Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces
复制标题
均匀贝索夫空间中两物种趋化系统的存在性和格夫瑞正则性
DOI：
10.1007/s11425-016-0490-y
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Sun JinYi
中科院分区：
文献类型：
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作者：
Yang MingHua;Fu ZunWei;Sun JinYi
研究了一类两种趋化模型的柯西问题。当初始数据（0,v0,w0）属于齐次Besov空间，且满足一定的技术假设时，利用傅里叶频率局部化和博尼副积分解，建立了解的唯一局部解和爆破判据。进一步证明了如果初始数据足够小，则解是全局的。同时，基于所谓的Gevrey估计，我们特别证明了解在空间变量上是解析的。此外，我们分析了解的长时间行为，并得到了Besov和Lebesgue空间中高导数的一些衰减估计。
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 spacesforp,qandrsatisfying 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.