论文标题
修改后的可压缩Navier-Stokes系统的渐近近似
Asymptotic approximation of a modified compressible Navier-Stokes system
论文作者
论文摘要
我们研究了受霍夫和祖布伦先前工作启发的经过改进的可压缩纳维尔 - 斯托克斯系统（MCNS）的长期渐近学。我们将动量场的新分解引入其不合转和不可压缩的部分中，并根据HERMITE函数近似热方程的解决方案来计算$ n^{th} $订单近似值，以使用$ n^{th} $顺序计算的解决方案。然后，我们获得了MCNS系统的解决方案的存在，并表明，在Hermite函数方面的近似值在长期渐近学中给出了领先的顺序项，并且在某些假设下可以明确评估。
We study the long time asymptotics of a modified compressible Navier-Stokes system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a new decomposition of the momentum field into its irrotational and incompressible parts, and a new method for approximating solutions of the heat equation in terms of Hermite functions in which $n^{th}$ order approximations can be computed for solutions with $n^{th}$ order moments. We then obtain existence of solutions to the mcNS system and show that the approximation in terms of Hermite functions gives the leading order terms in the long-time asymptotics, and under certain assumptions can be evaluated explicitly.
