论文标题
具有潜在力的完全可压缩纳维尔 - 螺旋杆方程的最佳衰减
Optimal decay of full compressible Navier-Stokes equations with potential force
论文作者
论文摘要
在本文中，我们旨在研究全局解决方案的高阶空间衍生物的最佳衰减率，以$ \ mathbb {r}^3 $中的潜在力为完整的可压缩Navier-Stokes（CNS）方程。我们建立了溶液本身及其空间衍生物的最佳衰减速率（包括具有潜在力的完整CNS方程的全局小解的最高空间衍生物）。随着被考虑的完整CNS方程中潜在力的存在，分析的难度来自非平凡的稳定溶液的出现。从某种意义上说，这些衰减速率确实是最佳的，它与布线化系统的溶液速率一致。此外，通过时间加权能量估计，光谱分析和高低频率分解来实现证明。
In this paper, we aim to investigate the optimal decay rate for the higher order spatial derivative of global solution to the full compressible Navier-Stokes (CNS) equations with potential force in $\mathbb{R}^3$. We establish the optimal decay rate of the solution itself and its spatial derivatives (including the highest order spatial derivative) for global small solution of the full CNS equations with potential force. With the presence of potential force in the considered full CNS equations, the difficulty in the analysis comes from the appearance of non-trivial ststionary solutions. These decay rates are really optimal in the sense that it coincides with the rate of the solution of the linerized system. In addition, the proof is accomplished by virtue of time weighted energy estimate, spectral analysis, and high-low frequency decomposition.
