Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces
Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces
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DOI：
10.1016/j.jde.2013.04.014
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Q. Jiu;Yi Wang;Z. Xin
中科院分区：
文献类型：
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作者：
Q. Jiu;Yi Wang;Z. Xin
本文研究了具有大初值和真空的二维可压缩Navier-Stokes方程Cauchy问题经典解的整体适定性。证明了：若剪切粘度μ为正常数，体粘度λ为密度的幂函数，即λ（ρ）=ρβ，β>3，则二维可压缩Navier-Stokes方程的Cauchy问题在整个空间R2上存在唯一的整体经典解（ρ，u），该解在R2的开集中可能包含真空.注意，初始数据可以任意大以包含真空状态。本文得到了密度和速度的各种加权估计，这些独立的估计反映了加权密度和加权速度随流动沿着传播的事实。
In this paper, we study the global well-posedness of classical solution to 2D Cauchy problem of the compressible Navier–Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ(ρ)=ρβwith β>3, then the 2D Cauchy problem of the compressible Navier–Stokes equations on the whole space R2admits a unique global classical solution (ρ,u) which may contain vacuums in an open set of R2. Note that the initial data can be arbitrarily large to contain vacuum states. Various weighted estimates of the density and velocity are obtained in this paper and these self-contained estimates reflect the fact that the weighted density and weighted velocity propagate along with the flow.