Existence and large time behavior to coupled chemotaxis-fluid equations in Besov-Morrey spaces
Existence and large time behavior to coupled chemotaxis-fluid equations in Besov-Morrey spaces
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Besov-Morrey 空间中耦合趋化流体方程的存在性和大时间行为
DOI：
10.1016/j.jde.2018.10.050
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发表时间：
2019
影响因子：
2.4
通讯作者：
Sun Jinyi
中科院分区：
文献类型：
--
作者：
Yang Minghua;Fu Zunwei;Sun Jinyi
本文研究了一类耦合趋化性-流体方程的Cauchy问题。利用方程的耦合结构，利用半群方法，在一定的技术假设下，证明了在小初值和外力（u 0，n 0，nc 0，c 0）∈ Nstecr 1，λ，∞− β 1× Nstecr 2，λ，∞− β 2× Nstecr 3，λ，∞− β 3× L∞，nc 0 ∈ MN − λ，λ的条件下方程解的存在性和渐近稳定性.对于函数空间之间的嵌入关系，我们表明，我们的初始数据类是大于Kozono等人。（2016）[11]并涵盖了点（Diracs）和细丝上初始聚集的物理情况。作为应用，我们得到了一类具有齐次初值的自相似解的吸引盆的渐近存在性。
The paper deals with the Cauchy problem of coupled chemotaxis-fluid equations. By taking advantage of a coupling structure of the equations and using the semigroup approach, we show existence and asymptotic stability with small initial data and external force (u 0, n 0,∇ c 0, c 0)∈ N˙ r 1, λ,∞− β 1× N˙ r 2, λ,∞− β 2× N˙ r 3, λ,∞− β 3× L∞,∇ ϕ∈ M N− λ, λ for certain technical assumptions. For the embedded relationship between function spaces, we show that our initial data class is larger than that of Kozono et al.(2016)[11] and covers physical cases of initial aggregation at points (Diracs) and on filaments. As an application, we obtain a class of asymptotically existence of a basin of attraction for each self-similar solutions with homogeneous initial data.