Global existence and time decay estimate of solutions to the Keller–Segel system
Global existence and time decay estimate of solutions to the Keller–Segel system
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DOI：
10.1002/mma.5352
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发表时间：
2018-11
影响因子：
2.9
通讯作者：
Zhong Tan;Jianfeng Zhou
中科院分区：
文献类型：
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作者：
Zhong Tan;Jianfeng Zhou
我们考虑整个空间中的趋化性-Navier-Stokes系统（Keller-Segel系统），它描述了氧气驱动的细菌，真核生物在流体中的运动。在小初值条件下，证明了R3中Cauchy问题解的整体存在性和时间衰减估计。当流体运动由Stokes方程描述时，当势函数λ很小且初始密度n 0（x）有有限质量时，我们在R2中建立了整体弱解.
We consider the chemotaxis‐Navier–Stokes system (Keller–Segel system) in the whole space, which describes the motion of oxygen‐driven bacteria, eukaryotes, in a fluid. We proved the global existence and time decay estimate of solutions to the Cauchy problem in R3 with the small initial data. Moreover, when the fluid motion is described by the Stokes equations, we established the global weak solutions to in R2 with the potential function ϕ is small and the initial density n0(x) has finite mass.