论文标题
非保守压缩两相流体模型的最佳衰减速率
Optimal decay rates of a non-conservative compressible two-phase fluid model
论文作者
论文摘要
我们关注的是，在整个空间R3中，强大溶液的时间衰减速率是非保守可压缩粘性两相流体模型的时间衰减率。与以前的相关作品相比，本文的主要新颖性在于，它提供了一个通用框架，可用于提取溶液的最佳衰减速率以及其从一阶到最高阶的全阶空间衍生物，与热方程相同。此外，对于精心选择的初始数据，我们还显示了衰减率的下限。我们的方法主要包括基于有限诱导的Hodge分解，低频和高频分解，精致的光谱分析和能量方法。
We are concerned with the time decay rates of strong solutions to a non-conservative compressible viscous two-phase fluid model in the whole space R3. Compared to the previous related works, the main novelty of this paper lies in the fact that it provides a general framework that can be used to extract the optimal decay rates of the solution as well as its all-order spatial derivatives from one-order to the highest-order, which are the same as those of the heat equation. Furthermore, for well-chosen initial data, we also show the lower bounds on the decay rates. Our methods mainly consist of Hodge decomposition, low-frequency and high-frequency decomposition, delicate spectral analysis and energy method based on finite induction.
