论文标题
可压缩的Navier-Stokes方程的强溶液的衰减，并具有大型初始数据
Decay of Strong Solution for the Compressible Navier-Stokes Equations with Large Initial Data
论文作者
论文摘要
在本文中，我们研究了全局大型解决方案与其相关的恒定平衡状态的收敛性，以及在三维整个空间中可压缩的Navier-Stokes方程的显式衰减率。假设初始数据属于某些负SOBOLEV空间，而不是Lebesgue空间，我们不仅证明了在时间演化中保留的溶液的负sobolev规范，而且还获得了与代数衰减率的全局大溶液与其相关的恒定平衡状态的收敛。此外，我们将表明，在$ l^2- $ norm中收集到零的全溶液的一阶空间衍生物的衰减速率是$（1+t）^{ - 5/4} $，与热方程相吻合。这扩展了以前的衰减率$（1+t）^{ - 3/4} $在\ cite {he-huang-wang2}中获得的。
In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the initial data belongs to some negative Sobolev space instead of Lebesgue space, we not only prove the negative Sobolev norms of the solution being preserved along time evolution, but also obtain the convergence of the global large solution to its associated constant equilibrium state with algebra decay rate. Besides, we shall show that the decay rate of the first order spatial derivative of large solution of the full compressible Navier-Stokes equations converging to zero in $L^2-$norm is $(1+t)^{-5/4}$, which coincides with the heat equation. This extends the previous decay rate $(1+t)^{-3/4}$ obtained in \cite{he-huang-wang2}.
