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Global Fujita-Kato solution of 3-D inhomogeneous incompressible Navier-Stokes system
Advances in Mathematics ( IF 1.7 ) Pub Date : 2020-03-01 , DOI: 10.1016/j.aim.2020.107007
Ping Zhang

In this paper, we shall prove the global existence of weak solutions to 3D inhomogeneous incompressible Navier-Stokes system $({\rm INS})$ with initial density in the bounded function space and having a positive lower bound and with initial velocity being sufficiently small in the critical Besov space, $\dot B^{\f12}_{2,1}.$ This result corresponds to the Fujita-Kato solutions of the classical Navier-Stokes system. The same idea can be used to prove the global existence of weak solutions in the \emph{critical functional framework} to $({\rm INS})$ with one component of the initial velocity being large and can also be applied to provide a lower bound for the lifespan of smooth enough solutions of $({\rm INS}).$

中文翻译:

3-D 非均匀不可压缩 Navier-Stokes 系统的全局 Fujita-Kato 解

在本文中,我们将证明 3D 非均匀不可压缩 Navier-Stokes 系统 $({\rm INS})$ 的弱解的全局存在性,其初始密度在有界函数空间中并且具有正下界且初始速度足够在临界 Besov 空间中很小,$\dot B^{\f12}_{2,1}.$ 这个结果对应于经典 Navier-Stokes 系统的 Fujita-Kato 解。同样的想法可以用来证明\emph{临界函数框架}到$({\rm INS})$ 的弱解的全局存在性,其中一个初始速度的分量很大,也可以应用于提供一个$({\rm INS}).$ 的足够平滑解的寿命下限
更新日期:2020-03-01
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