Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier-Stokes equations with vacuum
Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier-Stokes equations with vacuum
复制标题
真空下二维密度相关纳维-斯托克斯方程柯西问题强解的全局存在性和大时间渐近行为
DOI：
10.1088/1361-6544/aab31f
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发表时间：
2018
期刊：
影响因子：
1.7
通讯作者：
Zhong Xin
中科院分区：
文献类型：
--
作者：
Lu Boqiang;Shi Xiaoding（施小丁）;Zhong Xin
本文研究了二维非齐次不可压Navier-Stokes方程的Cauchy问题。证明了当初始密度在无穷远处衰减不太慢时，整个空间上依赖于密度的二维Navier-Stokes方程的Cauchy问题存在唯一的整体强解.注意，初始数据可以是任意大的，初始密度可以包含真空态，甚至有紧支撑。此外，我们还得到了速度和压力的空间梯度的大的时间衰减率，这是相同的均匀的情况下。
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.