Existence and uniqueness theorem on mild solutions to the Keller–Segel system coupled with the Navier–Stokes fluid
Existence and uniqueness theorem on mild solutions to the Keller–Segel system coupled with the Navier–Stokes fluid
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DOI：
10.1016/j.jfa.2015.10.016
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发表时间：
2016-03
影响因子：
1.7
通讯作者：
H. Kozono;M. Miura;Y. Sugiyama
中科院分区：
文献类型：
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作者：
H. Kozono;M. Miura;Y. Sugiyama
摘要我们在全空间中考虑与Navier-Stokes流体耦合的Keller-Segel方程组，在尺度不变空间中证明了具有小初值的整体温和解的存在性。我们的方法是基于隐函数定理，产生必要的连续依赖的解决方案的初始数据。作为一个副产品，我们显示的渐近稳定性的解决方案的时间到无穷大。由于我们可以在弱Lp-空间中处理初始数据，因此当初始数据是小的齐次函数时，自相似解的存在性。
Abstract We consider the Keller–Segel system coupled with the Navier–Stokes fluid in the whole space, and prove the existence of global mild solutions with the small initial data in the scaling invariant space. Our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data. As a byproduct, we show the asymptotic stability of solutions as the time goes to infinity. Since we may deal with the initial data in the weak L p-spaces, the existence of self-similar solutions provided the initial data are small homogeneous functions.